A Class of P-Matrices with Applications to the Localization of the Eigenvalues of a Real Matrix
Author:
- 1 January 2001
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 22 (4) , 1027-1037
Abstract
A matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row means is called a B-matrix. It is proved that the class of B-matrices is a subset of the class of P-matrices. Properties of B-matrices are used to localize the real eigenvalues of a real matrix and the real parts of all eigenvalues of a real matrix.Keywords
This publication has 9 references indexed in Scilit:
- Linear conditions for positive determinantsLinear Algebra and its Applications, 1999
- Backward stability of a pivoting strategy for sign-regular linear systemsBIT Numerical Mathematics, 1997
- Regions in the Complex Plane Containing the Eigenvalues of a MatrixThe American Mathematical Monthly, 1994
- Regions in the Complex Plane Containing the Eigenvalues of a MatrixThe American Mathematical Monthly, 1994
- Totally positive matricesLinear Algebra and its Applications, 1987
- Matrix Analysis1985
- Minimal Gerschgorin setsPacific Journal of Mathematics, 1965
- On the nonsingularity of real matricesMathematics of Computation, 1965
- Note on circular disks containing the eigenvalues of a matrixDuke Mathematical Journal, 1958