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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The variety of pairs of matrices with rank $ (AB-BA)\leq 1$


Author: Michael G. Neubauer
Journal: Proc. Amer. Math. Soc. 105 (1989), 787-792
MSC: Primary 14A25; Secondary 14A10, 15A30
MathSciNet review: 931743
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0931743-4
PII: S 0002-9939(1989)0931743-4
Article copyright: © Copyright 1989 American Mathematical Society