On the dimension of some real, bounded rank, matrix spaces

2009/11/10 by Andrea Causin, Causin, Andrea
Mathematics · #15A30 (55N15 #19L64) #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.KT #msc:15A30

paper · pdf · doi:10.48550/arxiv.0911.1810

7 pages

arxiv created 2009/11/10 · openalex publication_date 2009/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given n integer, let X be either the set of hermitian or real n× n matrices of rank at least n-1. If n is even, we give a sharp estimate on the maximal dimension of a real vector subspace of X∪\0\. The rusults are obtained, via K-theory, by studying a bundle map induced by the adjugation of matrices

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