Integer matrix factorisations, superalgebras and the quadratic form\n obstruction

2021/03/06 by Nicholas J. Higham, Higham, Nicholas J., Matthew C. Lettington +3
Computer Science · Engineering · Mathematics · #05B15 #11H55 #15A23 #15CA30 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2103.04149

openalex publication_date 2021/03/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We identify and analyse obstructions to factorisation of integer matrices\ninto products N^T N or N² of matrices with rational or integer entries.\nThe obstructions arise as quadratic forms with integer coefficients and raise\nthe question of the discrete range of such forms. They are obtained by\nconsidering matrix decompositions over a superalgebra. We further obtain a\nformula for the determinant of a square matrix in terms of adjugates of these\nmatrix decompositions, as well as identifying a it co-Latin symmetry space.\n

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