Clément de Seguins Pazzis

activity

20182026

collaborators

9 papers

math.RA2026

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

Clément de Seguins Pazzis

Given a field $F$ and an integer $n \geq 2$ , denote by $t_{n} (F)$ the greatest possible dimension for a vector space of $n$ -by- $n$ matrices over $F$ in whi…

math.RA2024

A connection between Schur and Dieudonné's theorems on spaces of bounded rank matrices

Clément de Seguins Pazzis

We use a double-duality argument to give a new proof of Dieudonné's theorem on spaces of singular matrices. The argument connects the situation to the structure of spaces of operat…

math.RA2024

On affine spaces of rectangular matrices with constant rank

Clément de Seguins Pazzis

Let $F$ be a field, and $n \geq p \geq r > 0$ be integers. In a recent article, Rubei has determined, when $F$ is the field of real numbers, the greatest possible d…

math.RA2023

Products of involutions in symplectic groups over general fields (I)

Clément de Seguins Pazzis

Let $s$ be an $n$ -dimensional symplectic form over an arbitrary field with characteristic not $2$ , with $n > 2$ . The simplicity of the group $Sp (s) / {\pm id}$ and…

math.RA2019

The structured Gerstenhaber problem (III)

Clément de Seguins Pazzis

Let $b$ be a symmetric bilinear form on a finite-dimensional vector space over a field with characteristic $2$ . Here, we determine the greatest possible dimension of a linear subsp…

math.RA2018

Products of involutions in the stable general linear group

Clément de Seguins Pazzis

In the stable general linear group over an arbitrary field, we prove that every element with determinant $\pm 1$ is the product of three involutions, and of no less in general. We…

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

A connection between Schur and Dieudonné's theorems on spaces of bounded rank matrices

On affine spaces of rectangular matrices with constant rank

Products of involutions in symplectic groups over general fields (I)

The structured Gerstenhaber problem (III)

Products of involutions in the stable general linear group

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