Some Results on Cross-Positive Matrices

Let K be a cone in Rⁿ, K1 its dual cone. An n×n matrix A is called cross-positive on K if and only if for all y?K, z?K1 such that (z, y) = 0 we have (z, Ay)?0. In this short note new equivalent conditions for matrices cross-positive on K will be given in terms of the partial ordering in Rⁿ induced by the cone K.