On some subclasses of <i>P</i>‐matrices

Abstract

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 &amp; Sons, Ltd.