A Canonical Form for Positive Definite Matrices

Mathieu Dutour Sikirić; Anna Haensch; John Voight; Wessel P. J. van Woerden

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arXiv · 2004.14022

A Canonical Form for Positive Definite Matrices

Mathieu Dutour Sikirić·Anna Haensch·John Voight·Wessel P. J. van Woerden

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Abstract

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension $n$, but it is practical and more efficient than canonical forms based on Minkowski reduction.

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Mathieu Dutour Sikirić, Anna Haensch, John Voight, Wessel P. J. van Woerden. 2020-04-29. A Canonical Form for Positive Definite Matrices. https://arxiv.org/abs/2004.14022

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