Wu, Lei The Re-positive definite solutions to the matrix inverse problem \(AX = B\). (English) Zbl 0754.15003 Linear Algebra Appl. 174, 145-151 (1992). 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 \(AX=B\). Reviewer: R.von Randow (Bonn) Cited in 1 ReviewCited in 18 Documents MSC: 15A09 Theory of matrix inversion and generalized inverses 15B48 Positive matrices and their generalizations; cones of matrices 15A24 Matrix equations and identities Keywords:matrix equation; Re-positive definite solution; real part; Re-positive definite matrices; matrix inverse problem; complex matrices PDF BibTeX XML Cite \textit{L. Wu}, Linear Algebra Appl. 174, 145--151 (1992; Zbl 0754.15003) OpenURL References: [1] Deif, A. S.: Normal positive definite matrices. Matrix tensor quart. 32, 109-110 (1982) · Zbl 0506.15013 [2] Guo, Z.: Criterion of positive definiteness of matrices and solution of inverse problem for system of linear equations. Chinese sci. Bull. 34, 89-94 (1989) · Zbl 0672.15007 [3] Johnson, C. R.; Neumann, M.: Square roots with positive definite Hermitian part. Linear and multilinear algebra 8, 353-355 (1980) · Zbl 0431.15011 [4] Kato, T.: Perturbation theory for linear operators. (1966) · Zbl 0148.12601 [5] Liang, J. -W.: Some inequalities concerning positive definite matrices. Math. practice theory, No. No. 1, 56-60 (1988) [6] Liu, J. -Z.; Xie, Q. -M.: An error in ”some inequalities concerning positive definite matrices”. Math. practice theory, No. No. 3, 82 (1989) [7] Sun, J. -G.: The stability of solutions for inverse problems of matrices. Math. numer. Sinica 8, 251-257 (1986) · Zbl 0607.65017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.