A note on irreducibility for linear operators on partially ordered finite dimensional vector spaces

AbstractMany of the important applications of the Perron-Frobenius theory of nonnegative matrices assume that certain matrices are irreducible. The purpose of this note is to introduce a weaker condition which can be used in place of irreducibility, even in the more general setting of linear operators on a partially ordered finite dimensional vector space. Applications to convergence theorems, comparison results, and generalized diagonal dominance conditions are given