[et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”4.27.0″ background_image=”https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-content\/uploads\/2024\/09\/GOPR0015-scaled.jpg” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_fullwidth_header title=”E2 212: Matrix Theory: Video Lectures and Notes” content_max_width=”none” module_class=”sub_header” _builder_version=”4.27.0″ title_font=”|on|||” title_text_color=”#FFFFFF” title_font_size=”50px” background_color=”rgba(255, 255, 255, 0)” background_image=”https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-content\/uploads\/2024\/09\/abstract-1438441.jpg” parallax=”on” button_one_letter_spacing_hover=”0″ button_two_letter_spacing_hover=”0″ global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”on” button_one_letter_spacing__hover=”0″ button_two_letter_spacing__hover_enabled=”on” button_two_letter_spacing__hover=”0″ button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off” theme_builder_area=”post_content”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”4.27.0″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_row _builder_version=”4.27.0″ _module_preset=”default” custom_padding=”|||0px||” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_column type=”4_4″ _builder_version=”4.27.0″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_text _builder_version=”4.27.0″ _module_preset=”default” text_orientation=”justified” custom_padding=”|||11px||” hover_enabled=”0″ global_colors_info=”{}” theme_builder_area=”post_content” sticky_enabled=”0″]<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"
Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 6: Determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_05_Part2_v2.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 6: Determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_07.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 6: Determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_09.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 6: Determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_12.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 6: Determinants.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_14.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 7: Properties of determinants, norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_16.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 8: Properties of norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_19.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 9: Dual norms, matrix norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_21.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 10: Properties of matrix norms, induced norms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_23.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 11: Induced norms, spectral radius.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_10_28.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 12: Properties of spectral radius, Banach lemma.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_02.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 13: Levy-Desplanques theorem, equivalence of matrix norms, errors in inverses of linear systems.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_04.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 14: Errors in inverses, errors in solving systems of linear equations.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_06.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 15: Eigenvalues and eigenvectors, the characteristic polynomial.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_09.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 16: Similar matrices, diagonalizability.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_11.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 17: Simultaneous diagonalizability, eigenvectors, principle of biorthogonality.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_13.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 18: Unitary matrices, unitary equivalence.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_20.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 19: Schur’s unitary triangularization theorem, Cayley-Hamilton theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_23.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 20: Uses of Cayley-Hamilton theorem, diagonalizability revisited, normal matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_25.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 21: Properties of normal matrices, QR decomposition, canonical forms.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_11_27.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 22: Jordan canonical form.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_02.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 23: Properties of the Jordan canonical form, convergent matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_04.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 24: Properties of convergent matrices, polynomials and matrices, Gaussian elimination.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_07.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 25: Gauss transforms, LU decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_09.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 26: LU decomposition with pivoting, LDM, LDLt decomposition.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_11.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 27: Cholesky decomposition, uses, Hermitian and symmetric matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_14.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 28: Properties of Hermitian matrices, variational characterization of eigenvalues, Rayleigh-Ritz theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_16.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 29: Courant-Fischer theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_18.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 30: Weyl’s theorem, eigenvalues of bordered matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_21.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 31: Interlacing theorems for Hermitian matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_23.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 32: Further interlacing theorems, majorization of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2020_12_30.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 33: Location and perturbation of eigenvalues: dominant diagonal theorem, Gersgorin disc theorem.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_01.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 34: Properties of Gersgorin discs, condition of eigenvalues.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_04.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 35: Perturbation of eigenvalues, Birkhoff’s theorem, Hoffman-Weilandt theorem.\u00a0Video1<\/a>,Video2<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_06.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 36: Singular value decomposition (SVD).\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_08.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 37: Properties of the SVD, generalized inverses of matrices.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_11.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n\nLecture 38: Least squares problems, generalized SVD theorem, constrained least squares.\u00a0Video<\/a>,\u00a0Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_13.svg\"){kind=link}
![Notes<\/a>.<\/div>\n<\/li>\n<\/ul>\n[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"Lecture 1: Basic definitions, vector space, basis.\u00a0Video,\u00a0Notes. Lecture 2: Basis, dimension, linear transforms, fundamental subspaces associated with a linear transform.\u00a0Video,\u00a0Notes. Lecture 3: Fundamental subspaces associated with a linear transform, rank.\u00a0Video,\u00a0Notes. Lecture 4: Rank, inner product, Cauchy-Schwarz inequality.\u00a0Video,\u00a0Notes. Lecture 5: Gram-Schmidt algorithm, determinants.\u00a0Video,\u00a0Notes. Lecture 6: Determinants.\u00a0Video,\u00a0Notes. Lecture 7: Properties of determinants, norms.\u00a0Video,\u00a0Notes. Lecture 8: Properties of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587"}],"collection":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/comments?post=987495587"}],"version-history":[{"count":2,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions"}],"predecessor-version":[{"id":987495590,"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/pages\/987495587\/revisions\/987495590"}],"wp:attachment":[{"href":"https:\/\/ece.iisc.ac.in\/~cmurthy\/wp-json\/wp\/v2\/media?parent=987495587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/ece.iisc.ac.in\/~cmurthy\/E2_212_Fall2020\/2021_01_15.svg\"){kind=link}