Gangster operators and invincibility of positive semidefinite matrices

Timothy Ferguson
Charles Johnson, William & Mary

Abstract

Decrease in absolute value of a symmetrically placed pair of off diagonal entries need not preserve positive definiteness of an n x n matrix, n >= 3. A gangster operator is one that replaces some such pairs by 0s. Circumstances in which gangster operators preserve positive definiteness are investigated. Certain general circumstances are given, and graphs that ensure preservation are characterized. (C)2010 Elsevier Inc. All rights reserved.