Solution to Several Split Quaternion Matrix Equations

Abstract

Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties. Then, via the real representation method, we obtain the necessary and sufficient conditions for the existence of solutions to two split quaternion matrix equations. In addition, two experimental examples are provided to show their feasibility.

Keywords

• split quaternions
• matrix equation
• real representation
• <i>η</i>-conjugate
• <i>η</i>-Hermitian