Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size

2022/12/16 by Duško Bogdanić, Alen Ðurić, Bogdanić, Duško +7
Computer Science · Engineering · Mathematics · #14L30 #15A21 #15A27 #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2212.08425

openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix B consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with B by characterizing the corresponding partitions.

Related

• Commuting Jordan Types: a Survey
• The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
• Jordan Type stratification of spaces of commuting nilpotent matrices
• On the maximum nilpotent orbit intersecting a centralizer in M(n,K)
• On the nilpotent commutator of a nilpotent matrix