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arXiv · 2109.10045

A Sylvester-type matrix equation over the Hamilton quaternions with an application

Long-Sheng Liu·Qing-Wen Wang·Mahmoud Saad Mehany
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Abstract

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves $\eta$-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.

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Long-Sheng Liu, Qing-Wen Wang, Mahmoud Saad Mehany. 2021-09-21. A Sylvester-type matrix equation over the Hamilton quaternions with an application. https://arxiv.org/abs/2109.10045

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