Author(s)

Yi Sun¹, Haibin Zhang², Chaoqian Li¹

¹School of Mathematics and Statistics, Yunnan University, Kunming, China.
²Jilin Vocational College of Industry and Technology, Jilin, China.

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.

Generalized Irreducible α-Matrices, H-Matrices, Irreducible, Nonsingular, Eigenvalues

Sun, Y. , Zhang, H. and Li, C. (2018) Generalized Irreducible α-Matrices and Its Applications. Advances in Linear Algebra & Matrix Theory, 8, 111-121. doi: 10.4236/alamt.2018.83010.