Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices

Yan Hong; Dongkyu Lim; Feng Qi

doi:10.1186/s13660-018-1749-0

Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices

J Inequal Appl. 2018;2018(1):155. doi: 10.1186/s13660-018-1749-0. Epub 2018 Jul 3.

Authors

Yan Hong¹, Dongkyu Lim², Feng Qi^{3

4

5}

Affiliations

¹ 1College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China.
² 2Department of Mathematics, Sungkyunkwan University, Suwon, South Korea.
³ 3Institute of Mathematics, Henan Polytechnic University, Jiaozuo, China.
⁴ 4Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, China.
⁵ 5Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China.

Abstract

In the paper, the authors establish some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices and modify shortcomings of some known inequalities for generalized eigenvalues in the related literature.

Keywords: Generalized eigenvalue; Hermitian matrix; Inequality; Perturbation problem.