Intervals of certain classes of \b{Z}-matrices

Abstract

Let A and B be M-matrices satisfying A ≤ B and J = [A, B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible Mmatrix and A ≤ B, then aA + bB is an invertible M-matrix for all a, b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.