On complex power nonnegative matrices

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-liketheory 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, theinverse of M-type matrices and the set of matrices whose columns (rows) sum up to one