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On some subclasses of P-matrices

✍ Scribed by Hou-Biao Li; Ting-Zhu Huang; Hong Li

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 155 KB
Volume: 14
Category: Article
ISSN: 1070-5325
DOI: 10.1002/nla.524

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✦ Synopsis

Abstract

A matrix with positive row sums and all its off‐diagonal elements bounded above by their corresponding row averages is called a B‐matrix by J. M. Peña in References (SIAM J. Matrix Anal. Appl. 2001; 22:1027–1037) and (Numer. Math. 2003; 95:337–345). In this paper, it is generalized to more extended matrices—MB‐matrices, which is proved to be a subclass of the class of P‐matrices. Subsequently, we establish relationships between defined and some already known subclasses of P‐matrices (see, References SIAM J. Matrix Anal. Appl. 2000; 21:67–78; Linear Algebra Appl. 2004; 393:353–364; Linear Algebra Appl. 1995; 225:117–123). As an application, some subclasses of P‐matrices are used to localize the real eigenvalues of a real matrix. Copyright © 2007 John Wiley & Sons, Ltd.

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