Cross-Positive Matrices

Abstract

Dedicated to Alslon HOllseholder on the occasion of his 65th birthdav. 1. Introduction. In recent years there has been a great deal of interest in a matrix A which is positive on a cone C in Euclidean n-space, i.e., AC s:;; C (e.g., Birkhoff [2] and Vandergraft [5]). Another type of positivity is considered by Haynsworth and Hoffman [4] for symmetric A and self-polar C. In this paper ( § 3) we introduce three classes of matrices related to the class of