Kronecker products of Perron similarities

TL;DR

This paper investigates Kronecker products of Perron similarities, providing methods to construct ideal Perron similarities with extremal rows, which are relevant to the nonnegative inverse eigenvalue problem.

Contribution

It introduces a novel analysis of Kronecker products of Perron similarities and constructs extremal Perron similarities, advancing understanding in nonnegative inverse eigenvalue problems.

Findings

Kronecker products preserve Perron similarity properties.

Constructed classes of extremal Perron similarities.

Enhanced tools for the nonnegative inverse eigenvalue problem.

Abstract

An invertible matrix is called a Perron similarity if one of its columns and the corresponding row of its inverse are both nonnegative or both nonpositive. Such matrices are of relevance and import in the study of the nonnegative inverse eigenvalue problem. In this work, Kronecker products of Perron similarities are examined and used to to construct ideal Perron similarities all of whose rows are extremal.