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Generalized Irreducible α-Matrices and Its Applications
School of Mathematics and Statistics, Yunnan University, Kunming, China
Jilin Vocational College of Industry and Technology, Jilin, China
School of Mathematics and Statistics, Yunnan University, Kunming, China
- 1 School of Mathematics and Statistics, Yunnan University, Kunming, China
- 2 Jilin Vocational College of Industry and Technology, Jilin, China
- 3 School of Mathematics and Statistics, Yunnan University, Kunming, China
Advances in Linear Algebra & Matrix Theory·Volume 08 (2018)·Pages 111–121·Published 8 August 2018·DOI10.4236/alamt.2018.83010
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Abstract
The class of generalized α-matrices is presented by Cvetković, L. (2006), and proved to be a subclass of H -matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H -matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H -matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.
KeywordsGeneralized Irreducible α-MatricesH-MatricesIrreducibleNonsingularEigenvalues
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