## 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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