Properties of Hermitian, Unitary, Positive Definite and Sparse Matrices

Patterns of different types of matrices.

This file : eig_svd_herm_unit_pos_def_2.m is a modified (improved) version of my previous file. The main correction has been to include issparse() instead of class() to identify a Sparse Matrix. This change is essential for R13.

The file eig_svd_herm_unit_pos_def_2.m and it's companion files contain the details of usage of commands like eig & eigs, svd & svds, and explains with many examples what a Hermitian Matrix is, what a Unitary Matrix is, what is meant by Positive Definite etc.

Given a matrix A, this pgm also determines the condition, calculates the Singular Values, the Hermitian Part and checks if the matrix is Positive Definite.

The 20 Test Cases of examples in the companion TEST file eig_svd_herm_unit_pos_def_2_TEST.m cover real, complex, Hermitian, Unitary, Hilbert, Pascal, Toeplitz, Hankel, Twiddle and Sparse matrices. This programme will be very useful for students who want to understand the concepts behind various types of matrices ; they get them all at one place - with many numerical examples / cases.

The third file : vandermonde_polyfit_twiddle_1.m has been included to generate Sparse Matrices for running Sparse Test Cases. It is a wonderful pgm for the exposition of FFT using Sparse Matrices.