Sums of two triangularizable quadratic matrices over an arbitrary field

DOI10.1016/j.laa.2011.11.026zbMath1253.15020arXiv1109.2255OpenAlexW1978787672MaRDI QIDQ417457

Clément de Seguins Pazzis

Publication date: 14 May 2012

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

Full work available at URL: https://arxiv.org/abs/1109.2255

zbMATH Keywords

idempotent matrixsquare-zero matrixcharacteristic twocompanion matricesquadratic sumrational canonical formtriangularizable quadratic matrices

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21)

Related Items (11)

Decompositions of matrices into diagonalizable and square-zero matrices ⋮ Decompositions of matrices into potent and square-zero matrices ⋮ On Some Decompositions of Matrices over Algebraically Closed and Finite Fields ⋮ Matrices over finite fields as sums of periodic and nilpotent elements ⋮ The sum and the product of two quadratic matrices: regular cases ⋮ The sum of two quadratic matrices: exceptional cases ⋮ The product of two invertible quadratic matrices: exceptional cases ⋮ The quadratic sum problem for symplectic pairs ⋮ A note on sums of three square-zero matrices ⋮ Products of Involutions of an Infinite-dimensional Vector Space ⋮ On the spectra of some combinations of two generalized quadratic matrices

Cites Work

• Sums of two square-zero matrices over an arbitrary field
• On linear combinations of two idempotent matrices over an arbitrary field
• Sums and products of two quadratic matrices
• When is a matrix a difference of two idempotents
• Sums of square-zero operators
• Elementary Divisors of AB and BA

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