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 \(AX=B\).


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


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