Solutions of the Dual Quaternion Matrix Equation AXB = C

doi:10.1007/s42967-025-00498-y

Abstract

Abstract: In this paper, we investigate the solutions to the dual quaternion matrix equation AXB=C, including the general solution, the solution containing only the standard part, and the solution containing only the dual part. First, we present the real representation matrix of the dual quaternion matrix and analyze the properties of its vector operator. Then we transform the dual quaternion matrix equation into a real linear system and give the equivalent condition for the existence of the solutions to the dual quaternion matrix equation AXB=C, which includes the general solution, the solution containing only the standard part, and the solution containing only the dual part. Furthermore, we obtain the expressions of these solutions and the minimal F^R-norm solutions to the dual quaternion matrix equation AXB=C. Finally, we propose the algorithms and conduct numerical experiments to verify the validity of our method.

Key words: Dual quaternion, Matrix equation, Real representation, Vector operator

Yinping Li, Ying Li, Xiaochen Liu, Ning Shao. Solutions of the Dual Quaternion Matrix Equation AXB = C[J]. Communications on Applied Mathematics and Computation, 2026, 8(4): 1268-1282.

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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-025-00498-y

https://www.camc.shu.edu.cn/EN/Y2026/V8/I4/1268

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Solutions of the Dual Quaternion Matrix Equation AXB = C

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