K. C. Sivakumar: Linear Algebra (IIT Madras)

# playlist of the 52 videos (click the up-left corner of the video)

source: nptelhrd       2015年2月5日
Mathematics - Linear Algebra by Dr. K. C. Sivakumar, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://nptel.ac.in

Mod-01 Lec-01 Introduction to the Course Contents. 26:47
Mod-01 Lec-02 Linear Equations 35:10
Mod-01 Lec-03a Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations 40:48
Mod-01 Lec-03b Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples 43:58
Mod-01 Lec-04 Row-reduced Echelon Matrices 48:23
Mod-01 Lec-05 Row-reduced Echelon Matrices and Non-homogeneous Equations 47:19
Mod-01 Lec-06 Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations 49:14
Mod-01 Lec-07 Invertible matrices, Homogeneous Equations Non-homogeneous Equations 50:58
Mod-02 Lec-08 Vector spaces 34:43
Mod-02 Lec-09 Elementary Properties in Vector Spaces. Subspaces 48:16
Mod-02 Lec-10 Subspaces (continued), Spanning Sets, Linear Independence, Dependence 43:25
Mod-03 Lec-11 Basis for a vector space 48:48
Mod-03 Lec-12 Dimension of a vector space 48:31
Mod-03 Lec-13 Dimensions of Sums of Subspaces 52:11
Mod-04 Lec-14 Linear Transformations 50:10
Mod-04 Lec-15 The Null Space and the Range Space of a Linear Transformation 51:04
Mod-04 Lec-16 The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces 41:45
Mod-04 Lec-17 Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I 47:34
Mod-04 Lec-18 Equality of the Row-rank and the Column-rank II 36:08
Mod-05 Lec19 The Matrix of a Linear Transformation 40:27
Mod-05 Lec-20 Matrix for the Composition and the Inverse. Similarity Transformation 47:04
Mod-06 Lec-21 Linear Functionals. The Dual Space. Dual Basis I 49:20
Mod-06 Lec-22 Dual Basis II. Subspace Annihilators I 38:53
Mod-06 Lec-23 Subspace Annihilators II 50:08
Mod-06 Lec-24 The Double Dual. The Double Annihilator 47:34
Mod-06 Lec-25 The Transpose of a Linear Transformation. Matrices of a Linear 45:22
Mod-07 Lec-26 Eigenvalues and Eigenvectors of Linear Operators 40:11
Mod-07 Lec-27 Diagonalization of Linear Operators. A Characterization 47:01
Mod-07 Lec-28 The Minimal Polynomial 42:38
Mod-07 Lec-29 The Cayley-Hamilton Theorem 47:21
Mod-08 Lec-30 Invariant Subspaces 39:19
Mod-08 Lec-31 Triangulability, Diagonalization in Terms of the Minimal Polynomial 51:30
Mod-08 Lec-32 Independent Subspaces and Projection Operators 48:42
Mod-09 Lec-33 Direct Sum Decompositions and Projection Operators I 48:49
Mod-09 Lec-34 Direct Sum Decomposition and Projection Operators II 46:40
Mod-10 Lec-35 The Primary Decomposition Theorem and Jordan Decomposition 38:51
Mod-10 Lec-36 Cyclic Subspaces and Annihilators 50:49
Mod-10 Lec-37 The Cyclic Decomposition Theorem I 49:56
Mod-10 Lec-38 The Cyclic Decomposition Theorem II. The Rational Form 46:12
Mod-11 Lec-39 Inner Product Spaces 44:44
Mod-11 Lec-40 Norms on Vector spaces. The Gram-Schmidt Procedure I 53:21
Mod-11 Lec-41 The Gram-Schmidt Procedure II. The QR Decomposition. 43:09
Mod-11 Lec-42 Bessel's Inequality, Parseval's Indentity, Best Approximation 41:53
Mod-12 Lec-43 Best Approximation: Least Squares Solutions 50:37
Mod-12 Lec-44 Orthogonal Complementary Subspaces, Orthogonal Projections 50:01
Mod-12 Lec-45 Projection Theorem. Linear Functionals 47:24
Mod-13 Lec-46 The Adjoint Operator 48:21
Mod-13 Lec-47 Properties of the Adjoint Operation. Inner Product Space Isomorphism 52:37
Mod-14 Lec-48 Unitary Operators 48:17
Mod-14 Lec-49 Unitary operators II. Self-Adjoint Operators I. 42:11
Mod-14 Lec-50 Self-Adjoint Operators II - Spectral Theorem 41:08
Mod-14 Lec-51 Normal Operators - Spectral Theorem 46:09

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