Matrix Analysis with Applications

This course is offered to UG and PG students of Engineering/Science background. It contains the concepts related to matrix theory and their applications in various disciplines. It covers a depth understanding of matrix computations involving rank, eigenvalues, eigenvectors, linear transformation, similarity transformations, (diagonalisation, Jordan canonical form, etc). It also involves various iterative methods, including Krylov subspace methods. Finally, topics like positive matrices, non-negative matrices and polar decomposition are discussed in detail with their applications.INTENDED AUDIENCE:UG and PG students of technical universities/collegesPREREQUISITES:NILINDUSTRY SUPPORT:NIL

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