On complex power nonnegative matrices. (English) Zbl 1310.15065
Summary: 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.
MSC:
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15B51 | Stochastic matrices |
Keywords:
nonnegative matrices; eventually nonnegative matrices; power nonnegative matrices; stochastic matrices; Perron-Frobenius theoryReferences:
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