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8 results on '"Xie, Lv‐ming"'

1. A system of dual quaternion matrix equations with its applications

Author

Xie, Lv-Ming and Wang, Qing-Wen

Subjects
Mathematics - Rings and Algebras, Mathematics - Numerical Analysis
Abstract

We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its general solution. Serving as an application, we investigate the solutions to the dual quaternion matrix equations $AX = B$ and $XC=D$, including $\eta$-Hermitian solutions. Lastly, we design a numerical example to validate the main research findings of this paper.

Published
2023

8. The (anti‐) η$$ \eta $$‐Hermitian solution to a novel system of matrix equations over the split quaternion algebra.

Author

Gao, Zi‐Han, Wang, Qing‐Wen, and Xie, Lv‐ming

Abstract

In comparison to quaternions, split quaternions exhibit a more intricate algebraic structure, characterized by the presence of nontrivial zero factors. Furthermore, in various fields such as geometry and electromagnetism, split quaternions serve as more convenient research tools than quaternions. This paper aims to establish the necessary and sufficient conditions for the existence of (anti‐) η$$ \eta $$‐Hermitian solutions to a novel system of matrix equations formulated over split quaternions. We also provide the general expression of such solutions when the system is solvable, along with the least squares (anti‐) η$$ \eta $$‐Hermitian solution in the case of inconsistency. To illustrate the key findings of this paper, numerical examples are presented. [ABSTRACT FROM AUTHOR]

Published
2024
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