On complex power nonnegative matrices
F. Tudisco, V. Cardinali, C. Di Fiore

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.
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Taxonomy
TopicsMatrix Theory and Algorithms · graph theory and CDMA systems · Advanced Topics in Algebra
