Solution of Inverse Eigenvalue Problem of Singular Hermitian Matrices of Rank Greater than or Equal to Four

Abstract

This work deals with a modification of an algorithm that solves a special Structured Inverse Eigenvalue Problems (SIEP). The problem we consider is the Structured Hermitian Inverse Eigenvalue Problem (SHIEP) where the researcher’s purpose is to find the solution of inverse eigenvalue problem of singular Hermitian matrix of rank greater than or equal to four. We modified an algorithm to generate singular symmetric and Hermitian matrices for rank greater than or equal to 4 that meet both the spectral and structural constraint as a solution for the inverse eigenvalue problem. Finally, we proved that given the spectrum and the scalars ki=1,2,…,𝑛−4, the inverse eigenvalue problem for an 𝑛 ×𝑛 singular symmetric and Hermitian matrices of rank 4 are solvable.