Sets of nonnegative matrices without positive products (Q426069)

Given a set of irreducible nonnegative matrices of order \(d \times d\), the authors study the problem of existence of a strictly positive product of these matrices, with repititions allowed. The main result of the article is that if the answer is in the negative then (under some rather general assumptions), there is a repetition of the set of standard basis vectors of \(\mathbb{R}^d\) on which all given the given matrices act as permutations.