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arXiv · 2506.12065

Segre Characteristic Equivalence

Jessie Pitsillides
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Abstract

Given only the dimension, $n$, of a square matrix $A \in M(n,\mathbb{C})$, how many Segre Characteristic equivalent matrices are there? Jordan Normal Form Theorem states that any linear operator over $\mathbb{C}$ is similar to a matrix in Jordan Normal Form. As such, this is a question of counting the number of possible Jordan Normal Forms for a given dimension. So, equivalently, how many Jordan Normal Forms can an $n\times n$ matrix possibly have?

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Jessie Pitsillides. 2025-06-01. Segre Characteristic Equivalence. https://arxiv.org/abs/2506.12065

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