An algorithm for the Cartan–Dieudonné theorem on generalized scalar product spaces

✍ Scribed by M.A. Rodrı´guez-Andrade; G. Aragón-González; J.L. Aragón; Luis Verde-Star

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 283 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.11.005

✦ Synopsis

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.