On complex power nonnegative matrices

TL;DR

This paper develops a Perron-Frobenius-like theory for complex matrices that have at least one nonnegative integer power, exploring their properties and relationships with other matrix classes.

Contribution

It introduces a novel theoretical framework for power nonnegative matrices, extending classical Perron-Frobenius theory to complex matrices with nonnegative powers.

Findings

Established a Perron-Frobenius-like theory for these matrices

Analyzed relationships with eventually nonnegative matrices

Explored connections with M-type matrices and stochastic matrices

Abstract

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.