A note on sums of three square-zero matrices

DOI10.1080/03081087.2016.1202187zbMath1360.15019arXiv1605.05131OpenAlexW2403268247MaRDI QIDQ2979460

Clément de Seguins Pazzis

Publication date: 25 April 2017

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05131

zbMATH Keywords

decompositionidempotent matricesfields with characteristic 2rational canonical formsquare-zero matrices

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

Related Items (12)

Sums and products of pairs of quadratic endomorphisms of a countable-dimensional vector space ⋮ Sums of square-zero endomorphisms of a free module. ⋮ The sum and the product of two quadratic matrices: regular cases ⋮ On the decompositions of infinite upper triangular matrices over rings ⋮ Products of involutions in the stable general linear group ⋮ The sum of two quadratic matrices: exceptional cases ⋮ Sum of two strictly n -zero matrices ⋮ Products of two involutions in orthogonal and symplectic groups ⋮ The Waring problem for matrix algebras ⋮ Unnamed Item ⋮ Commutators and images of noncommutative polynomials ⋮ Endomorphisms of free modules as sums of four quadratic endomorphisms

Cites Work

• Sums of two triangularizable quadratic matrices over an arbitrary field
• Sums of two square-zero matrices over an arbitrary field
• On linear combinations of two idempotent matrices over an arbitrary field
• On decomposing any matrix as a linear combination of three idempotents
• On sums of idempotent matrices over a field of positive characteristic
• On sums of three square-zero matrices
• Sums of nilpotent matrices
• On Similarity and the Diagonal of a Matrix

This page was built for publication: A note on sums of three square-zero matrices