One consequence of the Perron–Frobenius Theorem on indecomposable positive matrices is that whenever an $$n\times n$$ n × n matrix A dominates a non-singular positive matrix, there is an integer k dividing n such that, after a permutation of basis, A is block-monomial with $$k\times k$$ k × k blocks. Furthermore, for suitably large exponents, the nonzero blocks of $$A^m$$ A m are strictly positive. We present an extension of this result for indecomposable semigroups of positive matrices.
Positivity – Springer Journals
Published: Mar 3, 2016
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