Matrix Equation’s Reflexive and Anti-Reflexive Solutions over Quaternions

Xin Liu; Kaiqi Wen; Yang Zhang

doi:10.3390/sym15010040

Symmetry (Dec 2022)

Matrix Equation’s Reflexive and Anti-Reflexive Solutions over Quaternions

Xin Liu,
Kaiqi Wen,
Yang Zhang

Affiliations

Xin Liu: Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Macau 999078, China
Kaiqi Wen: Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Macau 999078, China
Yang Zhang: Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

DOI: https://doi.org/10.3390/sym15010040
Journal volume & issue: Vol. 15, no. 1
p. 40

Abstract

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We consider when the quaternion matrix equation AXB+CXD=E has a reflexive (or anti-reflexive) solution with respect to a given generalized reflection matrix. We adopt a real representation method to derive the solutions when it is solvable. Moreover, we obtain the explicit expressions of the least-squares reflexive (or anti-reflexive) solutions.

Published in Symmetry

ISSN: 2073-8994 (Online)
Publisher: MDPI AG
Country of publisher: Switzerland
LCC subjects: Science: Mathematics
Website: http://www.mdpi.com/journal/symmetry/

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