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The generalized anti-reflexive solutions for a class of matrix equations \((BX=C,XD=E)\). (English) Zbl 1157.15013

Authors’ summary: The generalized anti-reflexive solution for matrix equations (\(BX = C\), \(XD = E\)), which arise in left and right inverse eigenpair problems, is considered. With the special properties of generalized anti-reflexive matrices, necessary and sufficient conditions for the solvability and a general expression of the solution are obtained. Furthermore, the related optimal approximation problem to a given matrix over the solution set is solved. In addition, the algorithm and the example to obtain the unique optimal approximation solution are given.

MSC:

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