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

2021/09/21 by Liu, Long-Sheng, Wang, Qing-Wen, Mehany, Mahmoud Saad
#15A03 #15A09 #15A24 #15B33 #15B57 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2109.10045

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 η-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.

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