The combinatorial structure of eventually nonnegative matrices

Abstract

In this paper it is shown that an eventually nonnegative matrix A whose index of zero is less than or equal to one, exhibits many of the same combinatorial properties as a nonnegative matrix. In particular, there is a positive integer g such that A g is nonnegative, A and A g have the same irreducible classes, and the transitive closure of the reduced graph of A is the same as the transitive closure of the reduced graph of A g . In this instance, many of the combinatorial properties of nonnegative matrices carry over to this subclass of the eventually nonnegative matrices.