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Numerical Linear Algebra

Numerical Linear Algebra. Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. This course covers lessons in basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of nonlinear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, Jacobi method for finding the eigenvalues of a given matrix. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, image processing, numerical analysis and dynamical systems etc. (from nptel.ac.in)

Lecture 31 - Matrix Norms

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Lecture 01 - Matrix Operations and Types of Matrices

Lecture 02 - Determinant of a Matrix

Lecture 03 - Rank of a Matrix

Lecture 04 - Vector Space

Lecture 05 - Vector Space (cont.)

Lecture 06 - Linear Dependence and Independence

Lecture 07 - Bases and Dimensions

Lecture 08 - Bases and Dimensions (cont.)

Lecture 09 - Linear Transformation

Lecture 10 - Linear Transformation (cont.)

Lecture 11 - Orthogonal Subspaces

Lecture 12 - Row Space, Column Space and Null Space

Lecture 13 - Eigenvalues and Eigenvectors

Lecture 14 - Eigenvalues and Eigenvectors (cont.)

Lecture 15 - Diagonalizable Matrices

Lecture 16 - Orthogonal Sets

Lecture 17 - Gram Schmidt Orthogonalization and Orthonormal 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

Lecture 26 - Conditioning and Condition Numbers (cont.)

Lecture 27 - Stability of Numerical Algorithms

Lecture 28 - Stability of Numerical Algorithms (cont.)

Lecture 29 - Vector Norms

Lecture 30 - Vector Norms (cont.)

Lecture 31 - Matrix Norms

Lecture 32 - Matrix Norms (cont.)

Lecture 33 - Convergent Matrices

Lecture 34 - Convergent Matrices (cont.)

Lecture 35 - Stability of Nonlinear System

Lecture 36 - Condition Number of A Matrix: Elementary Properties

Lecture 37 - Sensitivity Analysis

Lecture 38 - Sensitivity Analysis (cont.)

Lecture 39 - Residual Theorem

Lecture 40 - Nearness to Singularity

Lecture 41 - Estimation of Condition Number

Lecture 42 - Singular Value Decomposition of a Matrix

Lecture 43 - Singular Value Decomposition of a Matrix (cont.)

Lecture 44 - Orthogonal Projections

Lecture 45 - Algebraic and Geometric Properties of Matrices using 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

Lecture 50 - Least Square Solutions (cont.)

Lecture 51 - Householder Matrices

Lecture 52 - Householder Matrices and their Applications

Lecture 53 - Householder QR Factorization

Lecture 54 - Householder QR Factorization (cont.)

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

Lecture 60 - Jacobi Method (cont.)