The Change of Basis Groupoid

2021/07/12 by D. A. Wolfram, Wolfram, D. A.
Mathematics · #33C45 #FOS: Mathematics #Primary 15A03 #Rings and Algebras (math.RA) #Secondary 20N02 #math.RA #msc:15A03 #msc:20N02 #msc:33C45

paper · pdf · doi:10.48550/arxiv.2107.05450

23 pages

arxiv created 2021/07/12 · arxiv updated 2021/07/13

Abstract

We show that the change of basis matrices of a set of m bases of a finite vector space is a connected groupoid of order m². We define a general method to express the elements of change of basis matrices as algebraic expressions using optimizations of evaluations of vector dot products. Examples are given with orthogonal polynomials.

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