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arXiv · 2305.00176

Canonical forms for a class of pairs of commuting nilpotent matrices under simultaneous similarity

Jiuzhao Hua
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Abstract

We present canonical forms for all indecomposable pairs $(A,B)$ of commuting nilpotent matrices over an arbitrary field under simultaneous similarity, where $A$ is the direct sum of two Jordan blocks with distinct sizes. We also provide the transformation matrix $X$ such that $(A, X^{-1}BX)$ is in its canonical form.

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Jiuzhao Hua. 2023-04-29. Canonical forms for a class of pairs of commuting nilpotent matrices under simultaneous similarity. https://arxiv.org/abs/2305.00176

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