2015/06/24 by Fredy Vides, Vides, Fredy
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Matrix Theory and Algorithms #math.GR #math.MG #math.OA #msc:15A24 #msc:15A60 #msc:15A83 #msc:47A20 #msc:47N40
paper · pdf · doi:10.48550/arxiv.1506.07470
arxiv created 2017/01/12 · arxiv updated 2017/01/16
In this document we study the local connectivity of the sets whose elements are m-tuples of pairwise commuting normal matrix contractions. Given ε>0, we prove that there is δ>0 such that for any two m-tuples of pairwise commuting normal matrix contractions X:=(X1,…,Xm) and X:=(X1,…,Xm) that are δ-close with respect to some suitable distance ð in (ℂn× n)m, we can find a m-tuple of matrix paths (homotopies) connecting X to \mathbfX relative to the intersection of some ε,ð-neighborhood of X with the set of m-tuples of pairwise commuting normal matrix contractions. One of the key features of these matrix homotopies is that δ can be chosen independent of n. Some connections with topology and numerical matrix analysis will be outlined as well.