Solution of inverse eigenvalue problem for singular symmetric and hermitian matrices of ranks five and six

Abstract

In this work, the inverse eigenvalue problem is studied in the context of singu lar symmetric and Hermitian matrices, with a particular emphasis on ranks five and six. We looked into ways to solve singular symmetric and Hermitian ma trices’ Inverse Eigenvalue Problem (IEP). We devised a method to reconstruct such matrices from their eigenvalues, based on a solvability lemma. Through innovative methodologies, we aim to provide effective solutions for determin ing the original matrices from their eigenvalues, shedding light on challenges posed by singularity and higher rank. In the case of n × n matrix, the number of independent matrix elements would reduced.