On the nilpotent commutator of a nilpotent matrix

Polona Oblak

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arXiv · 1106.1545

On the nilpotent commutator of a nilpotent matrix

Polona Oblak

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Abstract

We study the structure of the nilpotent commutator $\nb$ of a nilpotent matrix $B$. We show that $\nb$ intersects all nilpotent orbits for conjugation if and only if $B$ is a square--zero matrix. We describe nonempty intersections of $\nb$ with nilpotent orbits in the case the $n \times n$ matrix $B$ has rank $n-2$. Moreover, we give some results on the maximal nilpotent orbit that $\nb$ intersects nontrivially.

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Polona Oblak. 2011-06-08. On the nilpotent commutator of a nilpotent matrix. https://arxiv.org/abs/1106.1545

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