The strong nilpotency index of a matrix

DOI10.1080/03081087.2013.784282zbMath1315.15031arXiv1203.6615OpenAlexW2111860114MaRDI QIDQ5495735

Michiel de Bondt

Publication date: 7 August 2014

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

Full work available at URL: https://arxiv.org/abs/1203.6615

zbMATH Keywords

linear dependencequasi-translationstrongly nilpotent matriceslinear triangularization

Mathematics Subject Classification ID

Jacobian problem (14R15) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (6)

Rational maps \(H\) for which \(K(th)\) has transcendence degree 2 over \(K\) ⋮ Homogeneous quasi-translations in dimension 5 ⋮ Some remarks on the Jacobian Conjecture and Drużkowski mappings ⋮ Quadratic polynomial maps with Jacobian rank two ⋮ Some Remarks on Polynomial Maps ⋮ Triangularization of Matrices and Polynomial Maps

Cites Work

• Keller's problem
• Power linear Keller maps of rank two are linearly triangularizable
• Homogeneization of locally nilpotent derivations and an application to \(k[X,Y,Z\)]
• Singular Hessians
• Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian conjecture
• Strong nilpotence holds in dimensions up to five only^∗
• On generalized strongly nilpotent matrices
• Noncommutative-nilpotent matrices and the jacobian conjecture

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