Lecture 1 - Matrix Operations and Types of Matrices
Lecture 2 - Determinant of a Matrix
Lecture 3 - Rank of a Matrix
Lecture 4 - Vector Space - I
Lecture 5 - Vector Space - II
Lecture 6 - Linear dependence and independence
Lecture 7 - Bases and Dimension - I
Lecture 8 - Bases and Dimension - II
Lecture 9 - Linear Transformation - I
Lecture 10 - Linear Transformation - II
Lecture 11 - Orthogonal Subspaces
Lecture 12 - Row Space, Column Space and Null Space
Lecture 13 - Eigen Values and Eigen Vectors - I
Lecture 14 - Eigen Values and Eigen Vectors - II
Lecture 15 - Diagonalizable Matrices
Lecture 16 - Orthogonal Sets
Lecture 17 - Gram Schmidt ortthogonalization and orthogonal bases
Lecture 18 - Introduction to Matlab
Lecture 19 - Sign Integer Representation
Lecture 20 - Computer Representation of Numbers
Lecture 21 - Floating Point Representation
Lecture 22 - Round-off Error
Lecture 23 - Error Propagation in Computer Arithmetic
Lecture 24 - Addition and Multiplication of Floating Point Numbers
Lecture 25 - Conditioning and Condition Numbers - I
Lecture 26 - Conditioning and Condition Numbers - II
Lecture 27 - Stability of Numerical Algorithms - I
Lecture 28 - Stability of Numerical Algorithms - II
Lecture 29 - Vector Norms - I
Lecture 30 - Vector Norms - II
Lecture 31 - Matrix Norms - I
Lecture 32 - Matrix Norms - II
Lecture 33 - Convergent Matrices - I
Lecture 34 - Convergent Matrices - II
Lecture 35 - Stability of non linear system
Lecture 36 - Condition number of a matrix: Elementary Properties
Lecture 37 - Sensitivity Analysis - I
Lecture 38 - Sensitivity Analysis - II
Lecture 39 - Residual Theorem
Lecture 40 - Nearness to Singularity
Lecture 41 - Estimation of the Condition Number
Lecture 42 - Singular value decomposition of a matrix - I
Lecture 43 - Singular value decomposition of a matrix - II
Lecture 44 - Orthonormal Projections
Lecture 45 - Algebraic and geometric properties of SVD
Lecture 46 - SVD and their applications
Lecture 47 - Perturbation theorem for singular values
Lecture 48 - Outer product expansion of a matrix
Lecture 49 - Least square solutions - I
Lecture 50 - Least square solutions - II
Lecture 51 - Householder matrices
Lecture 52 - Householder matrices and their applications
Lecture 53 - Householder QR factorization - I
Lecture 54 - Householder QR factorization - II
Lecture 55 - Basic theorems on eigenvalues and QR method
Lecture 56 - Power Method
Lecture 57 - Rate of Convergence of Power Method
Lecture 58 - Applications of Power Method with Shift
Lecture 59 - Jacobi Method - I
Lecture 60 - Jacobi Method - II
