English

The Change of Basis Groupoid

Rings and Algebras 2021-07-13 v1

Abstract

We show that the change of basis matrices of a set of mm bases of a finite vector space is a connected groupoid of order m2m^2. 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.

Keywords

Cite

@article{arxiv.2107.05450,
  title  = {The Change of Basis Groupoid},
  author = {D. A. Wolfram},
  journal= {arXiv preprint arXiv:2107.05450},
  year   = {2021}
}

Comments

23 pages

R2 v1 2026-06-24T04:06:26.085Z