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A representation of the general common solution to the matrix equations $A_1XB_1=C_1$ and $A_2XB_2=C_2$ with applications. (English) Zbl 0983.15016
New necessary and sufficient conditions are derived for a pair of matrix equations $A_1XB_1=C_1$ and $A_2XB_2=C_2$ to have a common solution. Then a new representation is derived for the general common solution. The result is used to determine conditions for the existence of a solution and a new representation of the general Hermitian solution to the matrix equation $AXB=C$ $(A,B$, and $C$ are known matrices over the complex field).

MSC:
15A24Matrix equations and identities
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References:
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