What about A,B if AB-BA and A commute

2011/03/22 by Gérald Bourgeois, Gerald Bourgeois, Bourgeois, Gerald
Mathematics · #15A22 #15A24 #Advanced Topics in Algebra #FOS: Mathematics #Random Matrices and Applications #Rings and Algebras (math.RA) #advanced mathematical theories #math.RA #msc:15A22 #msc:15A24

paper · pdf · doi:10.48550/arxiv.1103.4200

3 pages

arxiv created 2011/03/22 · openalex publication_date 2011/03/22 · arxiv updated 2011/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A,B be complex n,n complex matrices such that AB-BA and A commute. We show that, if n=2 then A,B are simultaneously triangularizable and if n>=3 then there exists such a couple A,B such that the pair (A,B) has not property L of Motzkin-Taussky and such that B and C are not simultaneously triangularizable.

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