A canonical form for positive definite matrices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Other literature type 29 Dec 2020Embargo end date: 01 Apr 2020 Croatia, Netherlands English Publisher:Mathematical Sciences PublishersJournal:Open Book Series, volume 4, pages 179-195 (issn: 2329-9061, eissn: 2329-907X,

Copyright policy )Funded by:EC | ALGSTRONGCRYPTO

Authors: M. Dutour Sikirić (Mathieu); A. Haensch (Anna); J. Voight (John); W.P.J. van Woerden (Wessel);

doi: 10.2140/obs.2020.4.179 , 10.48550/arxiv.2004.14022

arXiv: 2004.14022

A canonical form for positive definite matrices

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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.

Countries

Croatia, Netherlands

Related Organizations

Centrum Wiskunde & Informatica
Netherlands
Dartmouth College
United States
Dutch Research Council
Netherlands
Duquesne University
United States

Keywords

positive definite matrix, graph isomorphism, Mathematics - Number Theory, Canonical form, Lattice isomorphism, Group Theory (math.GR), quadratic form, Graph isomorphism, canonical form ; quadratic form ; positive definite matrix ; lattice isomorphism ; graph isomorphism, Positive definite matrix, canonical form, Quadratic form, FOS: Mathematics, 11H55, 05E18, 05C60, Number Theory (math.NT), lattice isomorphism, Mathematics - Group Theory

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