(R, S)-(Skew) Symmetric Solutions to Matrix Equation AXB = C over Quaternions-Reference-Cited by-同舟云学术

(R, S)-(Skew) Symmetric Solutions to Matrix Equation AXB = C over Quaternions

Published:2024-01-18 Issue:2 Volume:12 Page:323
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Liao Ruopeng¹^ORCID,Liu Xin²^ORCID,Long Sujuan³,Zhang Yang⁴

Affiliation:

1. School of Computer Science and Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau 999078, China

2. Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau 999078, China

3. School of Mathematics and Data Science, Minjiang University, Fujian 350108, China

4. Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

Abstract

(R,S)-(skew) symmetric matrices have numerous applications in civil engineering, information theory, numerical analysis, etc. In this paper, we deal with the (R,S)-(skew) symmetric solutions to the quaternion matrix equation AXB=C. We use a real representation Aτ to obtain the necessary and sufficient conditions for AXB=C to have (R,S)-(skew) symmetric solutions and derive the solutions when it is consistent. We also derive the least-squares (R,S)-(skew) symmetric solution to the above matrix equation.

Funder

Macao Science and Technology Development Fund

National Natural Science Foundation of China

Natural Sciences and Engineering Research Council of Canada

Joint Research and Development Fund ofWuyi University, Hong Kong and Macao

MUST Faculty Research

Science Foundation of Fujian Province

Research Foundation of Minjiang University for the Introduction of Talents

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/2/323/pdf

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