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Reflexive solution to a system of matrix equations. (English) Zbl 1141.15319
Summary: We derive necessary and sufficient conditions for the existence and an expression of the (anti) reflexive solution with respect to the nontrivial generalized reflection matrix $$P$$ to the system of complex matrix equations $$AX=B$$ and $$XC=D$$. The explicit solutions of the approximation problem $$\min\limits_{X\in \phi}\|X-E\|_F$$ is given, where $$E$$ is a given complex matrix and $$\phi$$ is the set of all reflexive (or antireflexive) solutions of the system mentioned above, and $$\|\cdot\|$$ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.

##### MSC:
 15A24 Matrix equations and identities 15B57 Hermitian, skew-Hermitian, and related matrices 15A09 Theory of matrix inversion and generalized inverses
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##### References:
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