The quaternion matrix equation ΣA
i
XB
i
=E |
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Authors: | Huang Liping |
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Institution: | (1) Department of Basic Sciences, Xiangtan Polytechnic University, 411201 Xiangtan, China |
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Abstract: | LetH
F
be the generalized quaternion division algebra over a fieldF with charF#2. In this paper, the adjoint matrix of anyn×n matrix overH
F
γ] is defined and its properties is discussed. By using the adjoint matrix and the method of representation matrix, this
paper obtains several necessary and sufficient conditions for the existence of a solution or a unique solution to the matrix
equation Σ
i=0
k
A
i
XB
i
=E overH
F
, and gives some explicit formulas of solutions.
Supported by the National Natural Science Foundation of China and Human |
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Keywords: | Generalized quaternion matrix Adjoint matrix Matrix equation Representation matrix |
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