The variety of pairs of matrices with rank(𝐴𝐵-𝐵𝐴)≤1

Neubauer, Michael G.

doi:10.1090/S0002-9939-1989-0931743-4

The variety of pairs of matrices with rank$(AB-BA)\leq 1$
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by Michael G. Neubauer

Proc. Amer. Math. Soc. 105 (1989), 787-792

DOI: https://doi.org/10.1090/S0002-9939-1989-0931743-4

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Abstract:

We will show that the variety of pairs of $n \times n$ matrices over an algebraically closed field with rank one commutator consists of $n - 1$ irreducible components each of dimension ${n^2} + 2n - 1$.

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