On some subclasses of P‐matrices
Copyright policy )On some subclasses of P‐matrices
AbstractA 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.
- University of Electronic Science and Technology of China China (People's Republic of)
Positive matrices and their generalizations; cones of matrices, \(P\)-matrix, \(M\)-matrix, \(H\)-matrix, \(B\)-matrix, eigenvalue localization, Inequalities involving eigenvalues and eigenvectors
Positive matrices and their generalizations; cones of matrices, \(P\)-matrix, \(M\)-matrix, \(H\)-matrix, \(B\)-matrix, eigenvalue localization, Inequalities involving eigenvalues and eigenvectors
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