Integer matrix factorisations, superalgebras and the quadratic form obstruction
| Autor: | Nicholas J. Higham, Matthew C. Lettington, Karl Michael Schmidt |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Pure mathematics Algebra and Number Theory Mathematics - Number Theory 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Square matrix Superalgebra Matrix (mathematics) Range (mathematics) Integer matrix Factorization Quadratic form 15A23 15CA30 11H55 05B15 FOS: Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Number Theory (math.NT) 0101 mathematics Mathematics Integer (computer science) |
| Zdroj: | Higham, N J, Lettington, M C & Schmidt, K M 2021, ' Integer matrix factorisations, superalgebras and the quadratic form obstruction ', Linear Algebra and its Applications, vol. 622, pp. 250-267 . https://doi.org/10.1016/j.laa.2021.03.028 |
| ISSN: | 0024-3795 |
| Popis: | We identify and analyse obstructions to factorisation of integer matrices into products $N^T N$ or $N^2$ 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 $\it co-Latin$ symmetry space. 20 Pages |
| Databáze: | OpenAIRE |
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