Realizing Sule\u{i}manova spectra via permutative matrices, II

TL;DR

This paper solves the real nonnegative inverse eigenvalue problem for a specific class of permutative matrices, extending previous results and providing new necessary and sufficient conditions for symmetric cases.

Contribution

It introduces a new sufficient condition for the symmetric nonnegative inverse eigenvalue problem and extends existing results to normalized lists.

Findings

Solved the inverse eigenvalue problem for a class of permutative matrices.

Extended Johnson and Paparella's result to include normalized lists.

Established a new necessary and sufficient condition for symmetric nonnegative inverse eigenvalues.

Abstract

In this work, the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix. The necessary and sufficient condition there is also shown to be sufficient for the symmetric nonnegative inverse eigenvalue problem. A result due to Johnson and Paparella [MR3452738, Linear Algebra Appl. 493 (2016), 281--300] is extended to include normalized lists that satisfy the new sufficient condition.