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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 07 - Bases and Dimensions

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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.)