Generalizing the notion of rank to noncommutative quadratic forms
Rings and Algebras
2019-10-22 v1
Abstract
In 2010, Cassidy and Vancliff extended the notion of a quadratic form on n generators to the noncommutative setting. In this article, we suggest a notion of rank for such noncommutative quadratic forms, where n = 2 or 3. Since writing an arbitrary quadratic form as a sum of squares fails in this context, our methods entail rewriting an arbitrary quadratic form as a sum of products. In so doing, we find analogs for 2 x 2 minors and determinant of a 3 x 3 matrix in this noncommutative setting.
Keywords
Cite
@article{arxiv.1910.09016,
title = {Generalizing the notion of rank to noncommutative quadratic forms},
author = {Michaela Vancliff and Padmini Veerapen},
journal= {arXiv preprint arXiv:1910.09016},
year = {2019}
}