TITLE:
Generalized Irreducible α-Matrices and Its Applications
AUTHORS:
Yi Sun, Haibin Zhang, Chaoqian Li
KEYWORDS:
Generalized Irreducible α-Matrices, H-Matrices, Irreducible, Nonsingular, Eigenvalues
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.8 No.3,
August
9,
2018
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.