Inequalities for generalized eigenvalues of quaternion matrices

Studying eigenvalues of square matrices is a traditional and fundamental direction in linear algebra. Quaternion matrices constitute an important and extensively useful subclass of square matrices. In the paper, the authors (1) introduce the concept of “generalized eigenvalues of quaternion matrix”; (2) give some properties of generalized eigenvalues for a regular quaternion matrix pair; (3) establish inequalities, the min–max theorem, and the perturbation theorem for generalized eigenvalues of a regular quaternion matrix pair; (4) and weaken conditions of Theorem 2.1 in a paper published in 2018 at the Journal of Inequalities and Applications.