An algorithm for the Cartan-Dieudonn\'e theorem on generalized scalar product spaces
Rings and Algebras
2021-11-05 v1
Abstract
We present an algorithmic proof of the Cartan-Dieudonn\'e theorem on generalized real scalar product spaces with arbitrary signature. We use Clifford algebras to compute the factorization of a given orthogonal transformation as a product of reflections with respect to hyperplanes. The relationship with the Cartan-Dieudonn\'e-Scherk theorem is also discussed in relation to the minimum number of reflections required to decompose a given orthogonal transformation.
Cite
@article{arxiv.1011.1027,
title = {An algorithm for the Cartan-Dieudonn\'e theorem on generalized scalar product spaces},
author = {M. A. Rodríguez-Andrade and G. Aragón-González and J. L. Aragón and Luis Verde-Star},
journal= {arXiv preprint arXiv:1011.1027},
year = {2021}
}
Comments
25 pages