Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Chandra Murthy
NPTEL Co-ordinating Institute : IISc Bangalore
NPTEL Lecture Count : 80
NPTEL Course Size : 6.5 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Course introduction and properties of matrices
Lecture 2 - Vector spaces
Lecture 3 - Basis, dimension
Lecture 4 - Linear transforms
Lecture 5 - Fundamental subspaces of a matrix
Lecture 6 - Fundamental theorem of linear algebra
Lecture 7 - Properties of rank
Lecture 8 - Inner product
Lecture 9 - Gram-schmidt algorithm
Lecture 10 - Orthonormal matrices definition
Lecture 11 - Determinant
Lecture 12 - Properties of determinants
Lecture 13 - Introduction to norms and inner products
Lecture 14 - Vector norms and their properties
Lecture 15 - Applications and equivalence of vector norms
Lecture 16 - Summary of equivalence of norms
Lecture 17 - Dual norms
Lecture 18 - Properties and examples of dual norms
Lecture 19 - Matrix norms
Lecture 20 - Matrix norms: Properties
Lecture 21 - Induced norms
Lecture 22 - Induced norms and examples
Lecture 23 - Spectral radius
Lecture 24 - Properties of spectral radius
Lecture 25 - Convergent matrices, Banach lemma
Lecture 26 - Recap of matrix norms and Levy-Desplanques theorem
Lecture 27 - Equivalence of matrix norms and error in inverses of linear systems
Lecture 28 - Errors in inverses of matrices
Lecture 29 - Errors in solving systems of linear equations
Lecture 30 - Introduction to eigenvalues and eigenvectors
Lecture 31 - The characteristic polynomial
Lecture 32 - Solving characteristic polynomials, eigenvectors properties
Lecture 33 - Similarity
Lecture 34 - Diagonalization
Lecture 35 - Relationship between eigenvalues of BA and AB
Lecture 36 - Eigenvector and principle of biorthogonality
Lecture 37 - Unitary matrices
Lecture 38 - Properties of unitary matrices
Lecture 39 - Unitary equivalence
Lecture 40 - Schur's triangularization theorem
Lecture 41 - Cayley-Hamilton theorem
Lecture 42 - Uses of cayley-hamilton theorem and diagonalizability revisited
Lecture 43 - Normal matrices: Definition and fundamental properties
Lecture 44 - Fundamental properties of normal matrices
Lecture 45 - QR decomposition and canonical forms
Lecture 46 - Jordan canonical form
Lecture 47 - Determining the Jordan form of a matrix
Lecture 48 - Properties of the Jordan canonical form - Part 1
Lecture 49 - Properties of the Jordan canonical form - Part 2
Lecture 50 - Properties of convergent matrices
Lecture 51 - Polynomials and matrices
Lecture 52 - Other canonical forms and factorization of matrices: Gaussian elimination and LU factorization
Lecture 53 - LU decomposition
Lecture 54 - LU decomposition with pivoting
Lecture 55 - Solving pivoted system and LDM decomposition
Lecture 56 - Cholesky decomposition and uses
Lecture 57 - Hermitian and symmetric matrix
Lecture 58 - Properties of hermitian matrices
Lecture 59 - Variational characterization of Eigenvalues: Rayleigh-Ritz theorem
Lecture 60 - Variational characterization of eigenvalues (Continued...)
Lecture 61 - Courant-Fischer theorem
Lecture 62 - Summary of Rayliegh-Ritz and Courant-Fischer theorems
Lecture 63 - Weyl's theorem
Lecture 64 - Positive semi-definite matrix, monotonicity theorem and interlacing theorems
Lecture 65 - Interlacing theorem - I
Lecture 66 - Interlacing theorem - II (Converse)
Lecture 67 - Interlacing theorem (Continued...)
Lecture 68 - Eigenvalues: Majorization theorem and proof
Lecture 69 - Location and perturbation of Eigenvalues - Part 1: Dominant diagonal theorem
Lecture 70 - Location and perturbation of Eigenvalues - Part 2: Gersgorin's theorem
Lecture 71 - Implications of Gersgorin disc theorem, condition of eigenvalues
Lecture 72 - Condition of eigenvalues for diagonalizable matrices
Lecture 73 - Perturbation of eigenvalues Birkhoff's theorem Hoffman-Weiland ttheorem
Lecture 74 - Singular value definition and some remarks
Lecture 75 - Proof of singular value decomposition theorem
Lecture 76 - Partitioning the SVD
Lecture 77 - Properties of SVD
Lecture 78 - Generalized inverse of matrices
Lecture 79 - Least squares
Lecture 80 - Constrained least squares