Zhang, Lei The solvability conditions for the inverse problem of symmetric nonnegative definite matrices. (English. Chinese original) Zbl 0973.15008 Chin. J. Numer. Math. Appl. 12, No. 1, 1-7 (1990); translation from Math. Numer. Sin. 11, No. 4, 337-343 (1989). Summary: We consider the following two problems: Problem A: Given \(X,B\in \mathbb{R}^{n\times m}\), find \(A\in P_n\) such that \[ AX=B, \] where \(P_n=\{A\in\mathbb{R}^{n\times n}\mid A=A^T\), \(x^T Ax\geq 0\), \(\forall x\in \mathbb{R}^n\}\). Problem B: Given \(A^*\in \mathbb{R}^{n\times n}\), find \(\widehat A\in S_E\) such that \[ \|A^*-\widehat A\|= \inf_{A\in S_E}\|A^*-A\|, \] where \(\|\cdot\|\) is Frobenius norm, and \(S_E\) is the solution set of Problem A. Necessary and sufficient conditions under which \(S_E\) is nonempty are studied. The general form of \(S_E\) is given. For Problem B, the expression of the solution is provided. Cited in 3 Documents MSC: 15A29 Inverse problems in linear algebra 15A18 Eigenvalues, singular values, and eigenvectors Keywords:solvability conditions; inverse problem; symmetric nonnegative definite matrices; inverse eigenvalue problem PDF BibTeX XML Cite \textit{L. Zhang}, Chin. J. Numer. Math. Appl. 12, No. 1, 1--7 (1989; Zbl 0973.15008); translation from Math. Numer. Sin. 11, No. 4, 337--343 (1989)