Almost commuting matrices with respect to the rank metric

Gábor Elek; Łukasz Grabowski

doi:10.4171/ggd/623

JournalsggdVol. 15, No. 3pp. 1059–1083

Almost commuting matrices with respect to the rank metric

Gábor Elek
Lancaster University, UK
Łukasz Grabowski
Lancaster University, UK

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Abstract

We show that if $A_{1}, A_{2}, \dots, A_{n}$ 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 $B_{1}$ , $B_{2}$ , $\dots$ , $B_{n}$ that are close to the matrices $A_{i}$ in the rank metric.

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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