On Hermitian Solutions of the Generalized Quaternion Matrix Equation AXB+CX D=E

The paper deals with the matrix equation AXB+CX D=E over the generalized quaternions. By the tools of the real representation of a generalized quaternion matrix, Kronecker product as well as vec-operator, the paper derives the necessary and sufficient conditions for the existence of a Hermitian solu...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021-01, Vol.2021
Main Authors: Tian, Yong, Liu, Xin, Yuan, Shi-Fang
Format: Article
Language:English
Subjects:
Mathematical problems
Operators (mathematics)
Quaternions
Online Access:Get full text
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Summary:The paper deals with the matrix equation AXB+CX D=E over the generalized quaternions. By the tools of the real representation of a generalized quaternion matrix, Kronecker product as well as vec-operator, the paper derives the necessary and sufficient conditions for the existence of a Hermitian solution and gives the explicit general expression of the solution when it is solvable and provides a numerical example to test our results. The paper proposes a unificated algebraic technique for finding Hermitian solutions to the mentioned matrix equation over the generalized quaternions, which includes many important quaternion algebras, such as the Hamilton quaternions and the split quaternions.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/1497335