A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

Long-Sheng Liu, Qing-Wen Wang and Mahmoud Saad Mehany
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Long-Sheng Liu: Department of Mathematics, Shanghai University, Shanghai 200444, China
Qing-Wen Wang: Department of Mathematics, Shanghai University, Shanghai 200444, China
Mahmoud Saad Mehany: Department of Mathematics, Shanghai University, Shanghai 200444, China

Mathematics, 2022, vol. 10, issue 10, 1-20

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.

Keywords: matrix equation; Hamilton quaternion; ? -Hermitian matrix; Moore–Penrose inverse; rank (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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