## The Re-positive definite solutions to the matrix inverse problem $$AX = B$$.(English)Zbl 0754.15003

Author’s summary: A complex matrix $$A$$ is termed Re-positive definite if the real part of $$x^*Ax$$ is positive for every nonzero complex vector $$x$$. This paper is concerned with constructing complex Re-positive definite matrices and solving the following matrix inverse problem: Given complex matrices $$X$$ and $$B$$, find the set of all complex Re-positive definite matrices $$A$$ such that $$AX=B$$.

### MSC:

 15A09 Theory of matrix inversion and generalized inverses 15B48 Positive matrices and their generalizations; cones of matrices 15A24 Matrix equations and identities

### References:

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