A real representation method for special least squares solutions of the quaternion matrix equation ( A X B , D X E ) = ( C , F ) " role="presentation"> ( A X B , D X E ) = ( C , F ) ( A X B , D X E ) = ( C , F ) (AXB, DXE) = (C, F)

AIMS Mathematics

article

Fengxia Zhang¹  Ying Li¹  Jianli Zhao¹ 

[1] College of Mathematical Science, Liaocheng University

关键词: quaternion matrix equation;    real representation;    quaternion centrohermitian matrix;    quaternion skew centrohermitian matrix;    least squares solution;   

DOI  :  10.3934/math.2022803

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this article, our interest is the quaternion matrix equation $ (AXB, DXE) = (C, F) $, and we study its minimal norm centrohermitian least squares solution and skew centrohermitian least squares solution. By applying of the real representation matrices of quaternion matrices and relative properties, we convert the quaternion least squares problems with constrained variables into the corresponding real least squares problems with free variables, and then we obtain the solutions of corresponding problems. The final results can be expressed only by real matrices and vectors, and thus the corresponding algorithms only involves real operations and avoid complex quaternion operations. Therefore, they are portable and convenient. In the end, we give two examples to verify the effectiveness of the purposed algorithms.

【 授权许可】

CC BY