Matrix functions that preserve the strong Perron-Frobenius property

TL;DR

This paper characterizes matrix functions that maintain the strong Perron-Frobenius property, using the real Jordan canonical form, providing insights into how matrix functions influence spectral properties.

Contribution

It introduces a characterization of matrix functions that preserve the strong Perron-Frobenius property based on the real Jordan canonical form.

Findings

Identifies conditions under which matrix functions preserve the property.

Provides a theoretical framework for analyzing spectral preservation.

Enhances understanding of matrix function impacts on spectral properties.

Abstract

In this note, we characterize matrix functions that preserve the strong Perron-Frobenius property using the real Jordan canonical form of a real matrix.