Higher-distance commuting varieties

Madeleine Elyze, Alexander Guterman, Ralph Morrison

Published 2018-11-23Version 1

The commuting variety of matrices over a given field is a well-studied object in linear algebra and algebraic geometry. As a set, it consists of all pairs of square matrices with entries in that field that commute with one another. In this paper we generalize the commuting variety by using the commuting distance of matrices. We show that over an algebraically closed or a real closed field, each of our sets does indeed form a variety.