Linear Algebra (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Dr. K.C. Sivakumar

NPTEL Co-ordinating Institute : IIT Madras

NPTEL Lecture Count : 51

NPTEL Course Size : 21 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Introduction to the Course Contents
Lecture 2 - Linear Equations
Lecture 3a - Equivalent Systems of Linear Equations I : Inverses of Elementary Row-operations, Row-equivalent matrices
Lecture 3b - Equivalent Systems of Linear Equations II : Homogeneous Equations, Examples
Lecture 4 - Row-reduced Echelon Matrices
Lecture 5 - Row-reduced Echelon Matrices and Non-homogeneous Equations
Lecture 6 - Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations
Lecture 7 - Invertible matrices, Homogeneous Equations Non-homogeneous Equations
Lecture 8 - Vector spaces
Lecture 9 - Elementary Properties in Vector Spaces. Subspaces
Lecture 10 - Subspaces (Continued...), Spanning Sets, Linear Independence, Dependence
Lecture 11 - Basis for a vector space
Lecture 12 - Dimension of a vector space
Lecture 13 - Dimensions of Sums of Subspaces
Lecture 14 - Linear Transformations
Lecture 15 - The Null Space and the Range Space of a Linear Transformation
Lecture 16 - The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces
Lecture 17 - Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank - I
Lecture 18 - Equality of the Row-rank and the Column-rank - II
Lecture 19 - The Matrix of a Linear Transformation
Lecture 20 - Matrix for the Composition and the Inverse. Similarity Transformation
Lecture 21 - Linear Functionals. The Dual Space. Dual Basis - I
Lecture 22 - Dual Basis II. Subspace Annihilators - I
Lecture 23 - Subspace Annihilators - II
Lecture 24 - The Double Dual. The Double Annihilator
Lecture 25 - The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose
Lecture 26 - Eigenvalues and Eigenvectors of Linear Operators
Lecture 27 - Diagonalization of Linear Operators. A Characterization
Lecture 28 - The Minimal Polynomial
Lecture 29 - The Cayley-Hamilton Theorem
Lecture 30 - Invariant Subspaces
Lecture 31 - Triangulability, Diagonalization in Terms of the Minimal Polynomial
Lecture 32 - Independent Subspaces and Projection Operators
Lecture 33 - Direct Sum Decompositions and Projection Operators - I
Lecture 34 - Direct Sum Decompositions and Projection Operators - II
Lecture 35 - The Primary Decomposition Theorem and Jordan Decomposition
Lecture 36 - Cyclic Subspaces and Annihilators
Lecture 37 - The Cyclic Decomposition Theorem - I
Lecture 38 - The Cyclic Decomposition Theorem - II. The Rational Form
Lecture 39 - Inner Product Spaces
Lecture 40 - Norms on Vector spaces. The Gram-Schmidt Procedure I
Lecture 41 - The Gram-Schmidt Procedure II. The QR Decomposition
Lecture 42 - Bessel's Inequality, Parseval's Indentity, Best Approximation
Lecture 43 - Best Approximation: Least Squares Solutions
Lecture 44 - Orthogonal Complementary Subspaces, Orthogonal Projections
Lecture 45 - Projection Theorem. Linear Functionals
Lecture 46 - The Adjoint Operator
Lecture 47 - Properties of the Adjoint Operation. Inner Product Space Isomorphism
Lecture 48 - Unitary Operators
Lecture 49 - Unitary operators - II. Self-Adjoint Operators - I.
Lecture 50 - Self-Adjoint Operators - II - Spectral Theorem
Lecture 51 - Normal Operators - Spectral Theorem