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

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
• <i>η</i>-Hermitian matrix
• Moore–Penrose inverse
• rank