## 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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### References:

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