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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:
15A24 Matrix equations and identities
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