Author

Clément de Seguins Pazzis

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Preprint Sep 2026

Range-compatible homomorphisms on Hermitian matrices

Let $\mathbb{D}$ be a division ring with an involution $x \mapsto x^\star$, and $n \geq 2$ be an integer. Denote by $\mathcal{H}_n(\mathbb{D})$ the set of all $n$-by-$n$ Hermitian matrices with entries in $\mathbb{D}$, and by $\mathcal{A}\mathcal{H}_n(\mathbb{D})$ the set of all matrices $A-A^\star$ with $A \in \mathca...

Clément de Seguins Pazzis · 0 citations

Preprint Aug 2026

Spaces of triangularizable matrices (III): Perfect non-quadratically closed fields with characteristic 2

Given a field $\mathbb{F}$ and an integer $n \geq 2$, denote by $t_n(\mathbb{F})$ the greatest possible dimension for a vector space of $n$-by-$n$ matrices over $\mathbb{F}$ in which every element is triangularizable. It was recently proved that $t_n(\mathbb{F})=\frac{n(n+1)}{2}$ if and only if $\mathbb{F}$ is not quad...

Clément de Seguins Pazzis · 0 citations