Abstract
We give new necessary and sufficient conditions for the existence of a common solution to the pair of linear matrix equations A 1 XB 1 = C 1 and A 2 XB 2 = C 2 and derive a new representation of the general common solution to these two equations. We apply this result to determine new necessary and sufficient conditions for the existence of an Hermitian solution and a representation of the general Hermitian solution to the matrix equation AXB = C.
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