Matrix Analysis with Applications

COURSE LAYOUT

Week 1  : Echelon form and Rank of a matrix, Solution of system of linear equations.
Week 2  : Vector spaces and their properties, subspaces, basis and dimension, linear transformations.
Week 3  : Eigen values and eigen vectors, Calyey Haminton theorem, diagonalization.
Week 4  : Special matrices, Gerschgorin theorem, inner product spaces, matrix norms and  Gram Schmidt Process
Week 5  : Normal and Positive Definite matrices, Quadratic forms with applications
Week 6  : Evaluation of matrix functions, SVD and its applications
Week 7  : Stationary and non-stationary iterative methods for linear system
Week 8  : Krylov subspace methods, analysis of positive and non-negative matrices, polar decomposition theorem