Solution to Several Split Quaternion Matrix Equations

Xin Liu, Tong Shi and Yang Zhang ()
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Xin Liu: Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau 999078, China
Tong Shi: Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China
Yang Zhang: Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

Mathematics, 2024, vol. 12, issue 11, 1-12

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; ? -conjugate; ? -Hermitian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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