The generalized reflexive solution for a class of matrix equations \( (AX=B, XC=D)\). (English) Zbl 1150.15006

Summary: In this article, the generalized reflexive solution of matrix equations \( (AX=B, XC=D)\) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.


15A24 Matrix equations and identities
15A09 Theory of matrix inversion and generalized inverses
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