Clément de Seguins Pazzis

activity

20092026

most citedOn sums of idempotent matrices over a field of positive characteristic

20 citations · 267 across the 55 of their papers we have counts for

collaborators

56 papers

math.RA2026

Range-compatible homomorphisms on Hermitian matrices

Clément de Seguins Pazzis

Let $D$ be a division ring with an involution $x \mapsto x^{⋆}$ , and $n \geq 2$ be an integer. Denote by $H_{n} (D)$ the set of all $n$ -by- $n$ Hermitian…

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.RA2023

The quadratic sum problem for symplectic pairs

Clément de Seguins Pazzis

Let $(b, u)$ be a pair consisting of a symplectic form $b$ on a finite-dimensional vector space $V$ over a field $F$ , and of a $b$ -alternating endomorphism $u$ of $V$ (i.e.…

math.RA2023

A note on bireflectional elements of an algebra

Clément de Seguins Pazzis

A classical theorem of Wonenburger, Djokovic, Hoffmann and Paige states that an element of the general linear group of a finite-dimensional vector space is the product of two invol…

math.RA2023★ 5 cited

Products of two involutions in orthogonal and symplectic groups

Clément de Seguins Pazzis

An element of a group is called bireflectional when it is the product of two involutions of the group (i.e. elements of order 1 or 2). If an element is bireflectional then it is co…

math.RT2022

Locally finite cycles of linear mappings in countable dimension

Clément de Seguins Pazzis

Let $n$ be a positive integer. An $n$ -cycle of linear mappings is an $n$ -tuple $(u_{1}, \dots, u_{n})$ of linear maps $u_1 \in \mathrm{Hom}(U_1,U_2),u_2 \in \mathrm{Hom}(U_2,U_3),\dots,u…

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…

math.RA2018

On the linear preservers of Schur matrix functionals

Clément de Seguins Pazzis

Let $F$ be a field and $f : S_{n} \to F ∖ {0}$ be an arbitrary map. The Schur matrix functional associated to $f$ is defined as $M \in…

math.RA2018

The structured Gerstenhaber problem (II)

Clément de Seguins Pazzis

Let $b$ be a non-degenerate symmetric (respectively, alternating) bilinear form on a finite-dimensional vector space $V$ , over a field with characteristic different from $2$ . In a…

math.RA2018

The structured Gerstenhaber problem (I)

Clément de Seguins Pazzis

Let $b$ be a symmetric or alternating bilinear form on a finite-dimensional vector space $V$ . When the characteristic of the underlying field is not $2$ , we determine the greatest…

math.GN2018

On the finite topology of a vector space and the domination problem for families of norms

Clément de Seguins Pazzis

Let $V$ be a real or complex vector space. The finite topology of $V$ consists of all the subsets $U$ for which the intersection $U \cap F$ is closed in $F$ for every finite-dimens…

math.RA2017★ 1 cited

The sum and the product of two quadratic matrices

Clément de Seguins Pazzis

Let $p$ and $q$ be polynomials with degree $2$ over an arbitrary field $F$ . In the first part of this article, we characterize the matrices that can be decomposed as $A + B$ …

math.RA2016

Sums of three quadratic endomorphisms of an infinite-dimensional vector space

Clément de Seguins Pazzis

Let $V$ be an infinite-dimensional vector space over a field. In a previous article, we have shown that every endomorphism of $V$ splits into the sum of four square-zero ones but a…

math.RA2016

Large spaces of symmetric or alternating matrices with bounded rank

Clément de Seguins Pazzis

Let $r$ and $n$ be positive integers such that $r < n$ , and $K$ be an arbitrary field. In a recent work, we have determined the maximal dimension for a linear subspace of $n…

math.RA2016

Sums of quadratic endomorphisms of an infinite-dimensional vector space

Clément de Seguins Pazzis

We prove that every endomorphism of an infinite-dimensional vector space splits as the sum of four idempotents and as the sum of four square-zero endomorphisms, a result that is op…

math.RA2015

Affine spaces of symmetric or alternating matrices with bounded rank

Clément de Seguins Pazzis

Let $r$ and $n$ be positive integers such that $r < n$ , and $K$ be an arbitrary field. We determine the maximal dimension for an affine subspace of $n$ by $n$ symmetric (or…

math.RA2015★ 6 cited

Large spaces of bounded rank matrices revisited

Clément de Seguins Pazzis

Let $n, p, r$ be positive integers with $n \geq p \geq r$ . A rank- $r$ subset of $n$ by $p$ matrices (with entries in a field) is a subset in which every matrix has rank les…

math.RA2015★ 2 cited

Range-compatible homomorphisms on spaces of symmetric or alternating matrices

Clément de Seguins Pazzis

Let $U$ and $V$ be finite-dimensional vector spaces over an arbitrary field $K$ , and $S$ be a linear subspace of the space $L (U, V)$ of all linear maps…

math.RA2015★ 2 cited

Quasi-range-compatible affine maps on large operator spaces

Clément de Seguins Pazzis

Let $U$ and $V$ be finite-dimensional vector spaces over an arbitrary field, and $S$ be a subset of the space $L (U, V)$ of all linear maps from $U$ to $V$ . A map…

math.RA2014★ 2 cited

Range-compatible homomorphisms over fields with two elements

Clément de Seguins Pazzis

Let $U$ and $V$ be finite-dimensional vector spaces over a (commutative) field $K$ , and $S$ be a linear subspace of the space $L (U, V)$ of all linear op…