On some subclasses of P‐matrices |
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| Authors: | Hou‐Biao Li Ting‐Zhu Huang Hong Li |
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| Institution: | 1. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of China;2. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of ChinaSchool of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of China=== |
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| 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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| Keywords: | P‐matrix B‐matrix M‐matrix H‐matrix eigenvalues localization |
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