NOC:Numerical Linear Algebra


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