On Hermitian Solutions of the Split Quaternion Matrix Equation AXB+CXD=E

In this paper, we discuss Hermitian solutions of split quaternion matrix equation A X B + C X D = E , where X is an unknown split quaternion Hermitian matrix, and A ,  B ,  C ,  D ,  E are known split quaternion matrices with suitable size. The objective of this paper is to establish a necessary and...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2017-12, Vol.27 (4), p.3235-3252
Main Authors: Yuan, Shi-Fang, Wang, Qing-Wen, Yu, Yi-Bin, Tian, Yong
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
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Summary:In this paper, we discuss Hermitian solutions of split quaternion matrix equation A X B + C X D = E , where X is an unknown split quaternion Hermitian matrix, and A ,  B ,  C ,  D ,  E are known split quaternion matrices with suitable size. The objective of this paper is to establish a necessary and sufficient condition for the existence of a solution and a solution formulas. Moreover, we provide numerical algorithms and numerical examples to exemplify the results.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-017-0806-y