The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra-Reference-Cited by-同舟云学术

The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra

Published:2024-04-18 Issue:4 Volume:16 Page:491
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Si Kai-Wen¹,Wang Qing-Wen¹²^ORCID

Affiliation:

1. Department of Mathematics Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China

2. Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China

Abstract

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX = C and XB = C. Finally, we provide a numerical example to demonstrate the findings of this paper.

Funder

National Natural Science Foundation of China

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/4/491/pdf

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