A characterization of trace zero symmetric nonnegative 5x5 matrices

TL;DR

This paper solves the symmetric nonnegative inverse eigenvalue problem for 5x5 matrices with zero trace, providing necessary and sufficient conditions for such matrices' eigenvalues.

Contribution

It offers a complete characterization of trace zero symmetric nonnegative 5x5 matrices, advancing understanding of SNIEP in this specific case.

Findings

Provides necessary and sufficient conditions for eigenvalues of trace zero symmetric nonnegative 5x5 matrices.

Completes the solution of SNIEP for this matrix size and trace condition.

Enhances theoretical understanding of eigenvalue constraints in nonnegative symmetric matrices.

Abstract

The problem of determining necessary and sufficient conditions for a set of real numbers to be the eigenvalues of a symmetric nonnegative matrix is called the symmetric nonnegative inverse eigenvalue problem (SNIEP). In this paper we solve SNIEP in the case of trace zero symmetric nonnegative 5x5 matrices.