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Hermitian nonnegative-definite and positive-definite solutions of the matrix equation {\(AXB=C\)}. (English) Zbl 1067.15009

The author considers the matrix equation \(AXB=C\) where the matrices \(A\), \(B\) and \(C\) are respectively \(m\times n\), \(n\times p\) and \(m\times p\). One looks for a Hermitian nonnegative-definite or positive-definite solution \(X\). The author gives necessary and sufficient conditions for the existence, and in the case of existence he gives a representation of the solutions. The proofs are based on an algorithm. The results are illustrated by a numerical example.

MSC:

15A24 Matrix equations and identities
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