The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix

DOI10.1080/03081080701571083zbMath1156.15011arXivmath/0701561OpenAlexW1969042883MaRDI QIDQ3535390

Polona Oblak

Publication date: 11 November 2008

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

Full work available at URL: https://arxiv.org/abs/math/0701561

zbMATH Keywords

Jordan canonical formdigraphscommuting matricesnilpotent matricesgeneric matrices

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Commutativity of matrices (15A27) Hermitian, skew-Hermitian, and related matrices (15B57) Directed graphs (digraphs), tournaments (05C20) Canonical forms, reductions, classification (15A21)

Related Items (10)

On the maximal nilpotent orbit that intersects the centralizer of a matrix ⋮ On the nilpotent commutator of a nilpotent matrix ⋮ Commuting nilpotent matrices and Artinian algebras. ⋮ Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix ⋮ The poset of the nilpotent commutator of a nilpotent matrix ⋮ The smallest part of the generic partition of the nilpotent commutator of a nilpotent matrix ⋮ Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit ⋮ Jordan forms for mutually annihilating nilpotent pairs ⋮ On pairs of commuting nilpotent matrices ⋮ Artinian algebras and Jordan type

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