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Volume 14
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Article

Solving a System of Sylvester-like Quaternion Matrix Equations

by
Ruo-Nan Wang
1,
Qing-Wen Wang
1,2,* and
Long-Sheng Liu
1
1
Department of Mathematics, Shanghai University, Shanghai 200444, China
2
Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Symmetry 2022, 14(5), 1056; https://doi.org/10.3390/sym14051056
Submission received: 2 April 2022 / Revised: 4 May 2022 / Accepted: 17 May 2022 / Published: 20 May 2022
(This article belongs to the Section Mathematics)
Versions Notes

Abstract

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the η-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper.
Keywords: Sylvester-type matrix equation; quaternion matrix; rank; Moore-Penrose inverse; η-Hermitian matrix Sylvester-type matrix equation; quaternion matrix; rank; Moore-Penrose inverse; η-Hermitian matrix

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MDPI and ACS Style

Wang, R.-N.; Wang, Q.-W.; Liu, L.-S. Solving a System of Sylvester-like Quaternion Matrix Equations. Symmetry 2022, 14, 1056. https://doi.org/10.3390/sym14051056

AMA Style

Wang R-N, Wang Q-W, Liu L-S. Solving a System of Sylvester-like Quaternion Matrix Equations. Symmetry. 2022; 14(5):1056. https://doi.org/10.3390/sym14051056

Chicago/Turabian Style

Wang, Ruo-Nan, Qing-Wen Wang, and Long-Sheng Liu. 2022. "Solving a System of Sylvester-like Quaternion Matrix Equations" Symmetry 14, no. 5: 1056. https://doi.org/10.3390/sym14051056

APA Style

Wang, R.-N., Wang, Q.-W., & Liu, L.-S. (2022). Solving a System of Sylvester-like Quaternion Matrix Equations. Symmetry, 14(5), 1056. https://doi.org/10.3390/sym14051056

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