A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application - Long-Sheng Liu; Qing-Wen Wang; Mahmoud Saad Mehany (Mathematics, 2022)
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 <semantics>η</semantics>-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.