Criterion of positive definiteness of matrices and solution of inverse problem for system of linear equations (Q1119990)

The author presents \(O(n^ 3)\) algorithms for solving the following problems: (a) check a given \(n\times n\) real matrix A (not necessarily symmetric) for positive definiteness; (b) given real n-vectors x and b such that \(x^ Tb>0\), find a real symmetric matrix A such that \(Ax=b.\)