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

Bogdanić, Duško (author), Ðurić, Alen (author), Koljančić, Sara (author), Oblak, Polona (author), Šivic, Klemen (author)

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.

• Language: English
• Keywords: nilpotent matrix, centralizer, nilpotent orbit
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science ; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 59-90
• Numbering: Vol. 690
• PID: 20.500.12556/RUL-155307
• UDC: 512.64
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2024.03.008
• COBISS.SI-ID: 190118403
• Publication date in RUL: 25.03.2024

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: North Holland
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

• Language: Slovenian
• Keywords: nilpotentna matrika, centralizator, nilpotentna orbita