Integer matrix factorisations, superalgebras and the quadratic form obstruction

Higham, Nicholas J., Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622 , pp. 250-267. 10.1016/j.laa.2021.03.028

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Abstract

We identify and analyse obstructions to factorisation of integer matrices into products or 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0024-3795
Date of First Compliant Deposit:	20 March 2021
Date of Acceptance:	20 March 2021
Last Modified:	07 May 2023 00:25
URI:	https://orca.cardiff.ac.uk/id/eprint/139966

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