Title

Gangster operators and invincibility of positive semidefinite matrices

Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2010

Volume

433

Issue

12-Nov

First Page

2096

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.

DOI

10.1016/j.laa.2010.07.002

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