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Zbl 1154.15019
Wang, Qing-Wen; Zhang, Hua-Sheng; Yu, Shao-Wen
On solutions to the quaternion matrix equation $AXB+CYD=E$. (English)
[J] Electron. J. Linear Algebra 17, 343-358, electronic only (2008). ISSN 1081-3810/e

Authors' summary: ``Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation $AXB+CYD =E$. Formulas are established for the extreme ranks of real matrices $X_i, Y_i, i = 1,\cdots, 4$, in a solution pair $X = X_1+X_2i+X_3j+X_4k$ and $Y = Y_1+Y_2i+Y_3j+Y_4k $ to this equation. Moreover, necessary and sufficient conditions are derived for all solution pairs $X$ and $Y$ of this equation to be real or pure imaginary, respectively. Some known results can be regarded as special cases of the results in this paper.'' One of the main techniques used is the embedding of the space of quaternion matrices into the space of real matrices.
[Sheng Chen (Harbin)]

MSC 2000:: *15A24 Matrix equations
15A03 Vector spaces
15A09 Matrix inversion
15A33 Matrices over special rings

Keywords: quaternion matrix equation; extreme rank; generalized inverse

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Zentralblatt MATH Berlin [Germany]