# Almost commuting matrices with respect to the rank metric

### Gábor Elek

Lancaster University, UK### Łukasz Grabowski

Lancaster University, UK

## Abstract

We show that if $A_1,A_2,\ldots, A_n$ are square matrices, each of them is either unitary or self-adjoint, and they almost commute with respect to the rank metric, then one can find commuting matrices $B_1$, $B_2$, $\ldots$, $B_n$ that are close to the matrices $A_i$ in the rank metric.

## Cite this article

Gábor Elek, Łukasz Grabowski, Almost commuting matrices with respect to the rank metric. Groups Geom. Dyn. 15 (2021), no. 3, pp. 1059–1083

DOI 10.4171/GGD/623