A Note on Irreducibility for Linear Operators on Partially Ordered Finite Dimensional Vector Spaces.

摘要

Many of the important applications of the Perron-Frobenius theory of non-negative 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.