On the stochastic powers of nonnegative reducible matrices (Q1821844)

Let \(A\geq 0\) be an \(n\times n\) reducible matrix in its normal form where \(A_ 1,...,A_ g\) are isolated (square and irreducible) and \(A_{g+1},...,A_ s\) are nonisolated. If \(A\) has a stochastic power (i.e. there is a smallest positive integer \(p\) such that \(A^ p\) is stochastic), then there are smallest positive integers \(p_ 1,...,p_ g\) such that \(A_ 1^{p_ 1},...,A_ g^{p_ g}\) are all stochastic and \(p\) is the least common multiple of \(p_ 1,...,p_ g\).