RAY PATTERNS OF MATRICES AND NONSINGULARITY

A complex matrix A is ray-nonsingular if det(X circle A) not equal 0 f or every matrix X with positive entries. A sufficient condition for ra y nonsingularity is that the origin is not in the relative interior of the convex hull of the signed transversal products of A. The concept of an isolated set of transversals is defined and used to obtain a nec essary condition for A to be ray-nonsingular. Some fundamental similar ities as well as differences between ray nonsingularity and sign nonsi ngularity are illustrated. (C) 1997 Elsevier Science Inc.