Solving \(XX^{tr}=A\) over the integers (Q1899416)

An algorithm for solving \(XX^T = A\), where \(X\) is an \(n \times k\) and \(A\) is an \(n \times n\) positive definite matrix. Theoretical background for the algorithm described was given by the author in [\((*)\)J. Numer. Theory 47, No. 3, 273-283 (1994; Zbl 0805.11031)]. However, the author tries to keep the present paper sufficiently independent of \((*)\) by giving the matrix arguments for the results used in this paper. The necessary theory and the basic algorithm are clearly formulated. The author concludes the paper with comments on some applications, adjusted strategies, and examples.