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 bases of a finite vector space is a connected groupoid of order . 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.
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