An algorithm for the Cartan-Dieudonné theorem on generalized scalar product spaces
arXiv:1011.1027 · doi:10.1016/j.laa.2010.11.005
Abstract
We present an algorithmic proof of the Cartan-Dieudonné 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-Dieudonné-Scherk theorem is also discussed in relation to the minimum number of reflections required to decompose a given orthogonal transformation.
arXiv comment25 pages