Integer matrix factorisations, superalgebras and the quadratic form obstruction

We identify and analyse obstructions to factorisation of integer matrices into products NTN or N2 of matrices with rational or integer entries. The obstructions arise as quadratic forms with integer coefficients and raise the question of the discrete range of such forms. They are obtained by conside...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2021-08, Vol.622, p.250-267
Main Authors: Higham, Nicholas J., Lettington, Matthew C., Schmidt, Karl Michael
Format: Article
Language:English
Subjects:
Adjugate matrix
Decomposition
Integer matrix factorisation
Integers
Latin squares
Linear algebra
Mathematical analysis
Matrix superalgebra
Obstructions
Quadratic forms
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We identify and analyse obstructions to factorisation of integer matrices into products NTN or N2 of matrices with rational or integer entries. The obstructions arise as quadratic forms with integer coefficients and raise the question of the discrete range of such forms. They are obtained by considering matrix decompositions over a superalgebra. We further obtain a formula for the determinant of a square matrix in terms of adjugates of these matrix decompositions, as well as identifying a co-Latin symmetry space.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.03.028