The General Solution to a Classical Matrix Equation <i>AXB</i> = <i>C</i> over the Dual Split Quaternion Algebra

Abstract

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX = C and XB = C. Finally, we provide a numerical example to demonstrate the findings of this paper.

Keywords

• dual split quaternion
• real representation
• matrix equation
• general solution