On some subclasses of P‐matrices
Hou‐Biao Li, Ting‐Zhu Huang, Hong Li · Numerical Linear Algebra with Applications · 2007
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.