Eventually nonnegative matrices are similar to seminonnegative matrices

AbstractIn this paper, it is shown that the necessary and sufficient conditions on the Jordan form of a seminonnegative matrix, identified by Zaslavsky and McDonald, are in fact necessary and sufficient conditions on the Jordan form of every eventually nonnegative matrix. Thus every eventually nonnegative matrix is similar to a seminonnegative matrix. In [Linear Algebra Appl. 372 (2003) 253], they show that several of the combinatorial properties of reducible nonnegative matrices carry over to reducible seminonnegative matrices. In this paper it is shown that a property on the index of cyclicity of an irreducible nonnegative matrix carries over to the seminonnegative matrices