Solving a System of Sylvester-like Quaternion Matrix Equations

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 applica...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 5; p. 1056
Main Authors Wang, Ruo-Nan, Wang, Qing-Wen, Liu, Long-Sheng
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 20.05.2022
Subjects
Algebra
Algorithms
Control theory
Mathematical analysis
Moore-Penrose inverse
quaternion matrix
Quaternions
rank
Sylvester-type matrix equation
η-Hermitian matrix
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14051056