A Canonical Form for Positive Definite Matrices

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 i...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Mathieu Dutour Sikirić, Haensch, Anna, Voight, John, Wessel P J van Woerden
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.11.2020
Subjects
Algorithms
Canonical forms
Enumeration
Integral transforms
Lattices (mathematics)
Mathematical analysis
Matrix methods
Subgroups
Vectors (mathematics)
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422