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Zbl 1190.15019
Wang, Qing-Wen; Zhang, Hua-Sheng; Song, Guang-Jing
A new solvable condition for a pair of generalized Sylvester equations. (English)
[J] Electron. J. Linear Algebra 18, 289-301, electronic only (2009). ISSN 1081-3810/e

Summary: A necessary and sufficient condition is given for the quaternion matrix equations $A_i X + Y B_i = C_i$ $(i=1,2)$ to have a pair of common solutions $X$ and $Y$. As a consequence, the results partially answer a question posed by {\it Y. H. Liu} [Comput. Math. Appl. 52, No.~6--7, 861--872 (2006; Zbl 1129.15009)].

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

Keywords: quaternion matrix equation; generalized Sylvester equation; generalized inverse; minimal rank; maximal rank

Citations: Zbl 1129.15009

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Zentralblatt MATH Berlin [Germany]