Symmetric Nonnegative 5x5 Matrices Realizing Previously Unknown Region

TL;DR

This paper introduces new symmetric nonnegative 5x5 matrix families that realize previously unknown spectral regions and proves their stability under perturbations, expanding understanding of nonnegative matrix eigenvalues.

Contribution

The paper presents new symmetric nonnegative 5x5 matrix families that realize a previously unknown spectral region and demonstrates their closure under perturbations.

Findings

New symmetric nonnegative 5x5 matrix families identified

These matrices realize a previously unknown spectral region

Matrix families are shown to be closed under perturbations

Abstract

In this paper we present some symmetric nonnegative 5x5 matrix families that realize a previously unknown region. We also prove that these and other symmetric nonnegative 5x5 matrix families are closed under perturbations first presented in W. Guo. Eigenvalues of nonnegative matrices. Linear Algebra and its Applications, 266:261-270, 1997.