Clément de Seguins Pazzis

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20102026

most citedThe space of all p-th roots of a nilpotent complex matrix is path-connected

1 citations · 1 across the 18 of their papers we have counts for

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14 papers · 1 filter

math.RA2026

Large affine spaces of symplectic forms

Clément de Seguins Pazzis

Let F be a field and V be a 2n-dimensional vector space over F. In a previous article, we have proved that if F has more than 2n-2 elements then the greatest possible dimension for…

math.RA2025

Affine subspaces of units in simple algebras

Clément de Seguins Pazzis

Let $A$ be a simple algebra over a field $F$ . Under a mild cardinality assumption on $F$ , we determine the greatest possible dimension for an $F$ -affine subspace of $A$ that is inc…

math.RA2025

The Free Hamilton Algebra

Clément de Seguins Pazzis

Over an arbitrary field $F$ , let $p$ and $q$ be monic polynomials with degree $2$ in $F [t]$ . The free Hamilton algebra of the pair $(p, q)$ is the free noncommutat…

math.RA2024

Spaces of triangularizable matrices

Clément de Seguins Pazzis

Let F be a field. We investigate the greatest possible dimension t_n(F) for a vector space of n-by-n matrices with entries in F and in which every element is triangularizable over…

math.RA2022

Sums of two square-zero selfadjoint or skew-selfadjoint endomorphisms

Clément de Seguins Pazzis

Let $V$ be a finite-dimensional vector space over a field $F$ , equipped with a symmetric or alternating non-degenerate bilinear form $b$ . When the characteristic of $\math…

math.RA2021

Sums and products of two quadratic endomorphisms of a countable-dimensional vector space

Clément de Seguins Pazzis

Let $V$ be a vector space with countable dimension over a field, and let $u$ be an endomorphism of it which is locally finite, i.e. $(u^{k} (x))_{k \geq 0}$ is linearly dependent for…