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 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. © 2010 Elsevier Inc. All rights reserved.
Rodríguez-Andrade, M. A., Aragón-González, G., Aragón, J. L., & Verde-Star, L. (2011). An algorithm for the Cartan-Dieudonné theorem on generalized scalar product spaces. Linear Algebra and Its Applications, 434(5), 1238–1254. https://doi.org/10.1016/j.laa.2010.11.005