On the sum of the dimension of a matrix subalgebra and its centralizer

2009/12/24 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Computer Science · Engineering · Mathematics · #15A45 #16S50 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:15A45 #msc:16S50

paper · pdf · doi:10.48550/arxiv.0912.4821

17 pages (withdrawn as it appears there is a much shorter proof available)

openalex publication_date 2009/12/24 · arxiv created 2010/04/05 · arxiv updated 2010/04/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

When \mathbbK is a field, and A and B denote commuting subspaces of M_n(\K) each of which contains a non-scalar matrix, we prove that dim A +dim B ≤ (n-1)²+3. We also give a complete description of the cases when equality holds.

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