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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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