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A new solvable condition for a pair of generalized Sylvester equations. (English) Zbl 1190.15019

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 Y. H. Liu [Comput. Math. Appl. 52, No. 6–7, 861–872 (2006; Zbl 1129.15009)].

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
15A03 Vector spaces, linear dependence, rank, lineability

Citations:

Zbl 1129.15009
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