Abstract
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.
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Acknowledgements
The authors thank anonymous referees for their careful corrections and valuable comments on the original version of this paper.
Funding
This work was partially supported by the National Natural Science Foundation of China (Grant No. 11361038), by the Foundation of the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (Grant No. NJZY19157), and by the Science Research Fund of Inner Mongolia University for Nationalities (Grant No. NMDBY15019 and No. NMDBY19056), China.
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Hong, Y., Qi, F. Inequalities for generalized eigenvalues of quaternion matrices. Period Math Hung 83, 12–19 (2021). https://doi.org/10.1007/s10998-020-00358-7
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DOI: https://doi.org/10.1007/s10998-020-00358-7