Michael Neubauer
Abstract
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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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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 ${n^2} + 2n - 1$.
Key concepts: Algebraically closed field, Rank (graph theory), Variety (cybernetics), Dimension (graph theory), Mathematics, Combinatorics, Commutator, Field (mathematics)