Solubility Existence of Inverse Eigenvalue Problem for a Class of Singular Hermitian Matrices

Abstract

In this article, we discuss singular Hermitian matrices of rank greater or equal to four for an inverse eigenvalue problem. Specifically, we look into how to generate n by n singular Hermitian matrices of ranks four and five from a prescribed spectrum. Numerical examples are presented in each case to illustrate these scenarios. It was established that given a prescribed spectral datum and it multiplies, then the solubility of the inverse eigenvalue problem for n by n singular Hermitian matrices of rank r exists.