Eventually nonnegative matrices are similar to seminonnegative matrices. (Q1430385)

Seminonnegative matrices are a subclass of the eventually nonnegative matrices that share many of the combinatorial properties of nonnegative matrices. In Section 3, the authors complete the characterization of the Jordan forms that are similar to eventually nonnegative matrices. In Section 4, they show that if an irreducible seminonnegative matrix is \(m\)-cyclic, then for every positive integer \(g\), \(A^g\) is permutationally similar to the direct sum of \(k\) irreducible matrices where \(k= \text{gcd}(g, m)\).