NOC:Matrix Analysis with Applications


Lecture 1 - Elementary row operations


Lecture 2 - Echelon form of a matrix


Lecture 3 - Rank of a matrix


Lecture 4 - System of Linear Equations - I


Lecture 5 - System of Linear Equations - II


Lecture 6 - Introduction to Vector Spaces


Lecture 7 - Subspaces


Lecture 8 - Basis and Dimension


Lecture 9 - Linear Transformations


Lecture 10 - Rank and Nullity


Lecture 11 - Inverse of a Linear Transformation


Lecture 12 - Matrix Associated with a LT


Lecture 13 - Eigenvalues and Eigenvectors


Lecture 14 - Cayley-Hamilton Theorem and Minimal Polynomial


Lecture 15 - Diagonalization


Lecture 16 - Special Matrices


Lecture 17 - More on Special Matrices and Gerschgorin Theorem


Lecture 18 - Inner Product Spaces


Lecture 19 - Vector and Matrix Norms


Lecture 20 - Gram Schmidt Process


Lecture 21 - Normal Matrices


Lecture 22 - Positive Definite Matrices


Lecture 23 - Positive Definite and Quadratic Forms


Lecture 24 - Gram Matrix and Minimization of Quadratic Forms


Lecture 25 - Generalized Eigenvectors and Jordan Canonical Form


Lecture 26 - Evaluation of Matrix Functions


Lecture 27 - Least Square Approximation


Lecture 28 - Singular Value Decomposition


Lecture 29 - Pseudo-Inverse and SVD


Lecture 30 - Introduction to Ill-Conditioned Systems


Lecture 31 - Regularization of Ill-Conditioned Systems


Lecture 32 - Linear Systems: Iterative Methods - I


Lecture 33 - Linear Systems: Iterative Methods - II


Lecture 34 - Non-Stationary Iterative Methods: Steepest Descent - I


Lecture 35 - Non-Stationary Iterative Methods: Steepest Descent - II


Lecture 36 - Krylov Subspace Iterative Methods (Conjugate Gradient Method)


Lecture 37 - Krylov Subspace Iterative Methods (CG and Pre-Conditioning)


Lecture 38 - Introduction to Positive Matrices


Lecture 39 - Positive Matrices, Positive Eigenpair, Perron Root and vector, Example


Lecture 40 - Polar Decomposition