On complex power nonnegative 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.

Please cite this work as:

@article{tudisco2015complex,
  title={On complex power nonnegative matrices},
  author={Tudisco, Francesco and Cardinali, Valerio and Di Fiore, Carmine},
  journal={Linear Algebra and its Applications},
  volume={471},
  pages={449--468},
  year={2015},
  publisher={Elsevier}
}

Keywords: Nonnegative matrices Eventually nonnegativity Power nonnegativity Stochastic matrices Perron-Frobenius theory