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On some subclasses of P ‐matrices
Author(s) -
Li HouBiao,
Huang TingZhu,
Li Hong
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.524
Subject(s) - mathematics , linear algebra , matrix (chemical analysis) , eigenvalues and eigenvectors , combinatorics , bounded function , integer matrix , class (philosophy) , diagonal matrix , matrix analysis , algebra over a field , diagonal , symmetric matrix , discrete mathematics , pure mathematics , nonnegative matrix , mathematical analysis , geometry , materials science , physics , quantum mechanics , artificial intelligence , computer science , composite material
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.