Geodesic
A new solvable condition for a pair of generalized Sylvester equations
The electronic journal of linear algebra, Tome 18 (2009), pp. 289-301.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A necessary and sufficient condition is given for the quaternion matrix equations Ai X + Y B i = Ci ( i = 1, 2) to have a pair of common solutions X and Y . As a consequence, the results partially answer a question posed by Y.H. Liu (Y.H. Liu, Ranks of solutions of the linear matrix equation AX + Y B = C, Comput. Math. Appl., 52 (2006), pp. 861-872).
Classification : 15A03, 15A09, 15A24, 15A33
Keywords: quaternion matrix equation, generalized Sylvester equation, generalized inverse, minimal rank, maximal rank 
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     author = {Wang, Qing-Wen and Zhang, Hua-Sheng and Song, Guang-Jing},
     title = {A new solvable condition for a pair of generalized {Sylvester} equations},
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     year = {2009},
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Wang, Qing-Wen; Zhang, Hua-Sheng; Song, Guang-Jing. A new solvable condition for a pair of generalized Sylvester equations. The electronic journal of linear algebra, Tome 18 (2009), pp. 289-301. http://geodesic.mathdoc.fr/item/ELA_2009__18__a32/