# On complex power nonnegative matrices

Francesco Tudisco,
Valerio Cardinali,
Carmine Di Fiore,

**Linear Algebra and its Applications**,
471 :
449--468
(2015)

### Abstract

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perronâ€“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}
}
```

**Links:**
doi
arxiv

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