This article is cited in 2 papers

Computation of unimodular matrices

A. D. Bruno, A. A. Azimov


Abstract: Here we give an algorithm for solving the following problem. Let $m<n$ integer vectors be given in the $n$-dimensional real space. Their linear span forms a linear subspace $L$ in $\mathbb{R}^n$. It is required to calculate such an unimodular matrix that a linear transformation with it transforms the subspace $L$ into a coordinate one. Also, programs that implement the algorithms and power transformations, for which they are needed, are given.

Keywords: unimodular matrix, integer vector, continued fraction, the Euler's algorithm, power transformation.

UDC: 517.36

DOI: 10.20948/prepr-2022-46