Solutions of the Dual Quaternion Matrix Equation AXB = C

doi:10.1007/s42967-025-00498-y

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (4): 1268-1282.doi: 10.1007/s42967-025-00498-y

Solutions of the Dual Quaternion Matrix Equation AXB = C

Yinping Li, Ying Li, Xiaochen Liu, Ning Shao

School of Mathematical Science, Liaocheng University, Liaocheng, 252000, Shandong, China

收稿日期:2024-11-07 修回日期:2025-03-30 接受日期:2025-04-02 出版日期:2026-08-20 发布日期:2026-09-17
通讯作者: Yinping Li, Email: liyingld@163.com E-mail:liyingld@163.com
基金资助:
This work is supported by the National Natural Science Foundation of China (Grant No. 62176112), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2022MA030), and the Discipline with Strong Characteristics of Liaocheng University-Intelligent Science and Technology (Grant No. 319462208).

Solutions of the Dual Quaternion Matrix Equation AXB = C

Yinping Li, Ying Li, Xiaochen Liu, Ning Shao

School of Mathematical Science, Liaocheng University, Liaocheng, 252000, Shandong, China

Received:2024-11-07 Revised:2025-03-30 Accepted:2025-04-02 Online:2026-08-20 Published:2026-09-17
Supported by:
This work is supported by the National Natural Science Foundation of China (Grant No. 62176112), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2022MA030), and the Discipline with Strong Characteristics of Liaocheng University-Intelligent Science and Technology (Grant No. 319462208).

摘要/Abstract

摘要： 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.

关键词: Dual quaternion, Matrix equation, Real representation, Vector operator

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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Solutions of the Dual Quaternion Matrix Equation AXB = C

Solutions of the Dual Quaternion Matrix Equation AXB = C

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