Ray patterns of matrices and nonsingularity

✍ Scribed by J.J. McDonald; D.D. Olesky; M.J. Tsatsomeros; P. van den Driessche

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 866 KB
• Volume: 267
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)80057-2

✦ Synopsis

A complex matrix A is ray-nonsingular if det(X 0 A) f 0 for every matrix X with positive entries. A sufficient condition for ray 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 neces-*Work supported by an NSERC research grant.