An algorithm for the Cartan-Dieudonne theorem on generalized scalar product spaces

作者：Rodriguez Andrade M A^*; Aragon Gonzalez G; Aragon J L; Verde Star Luis

来源：Linear Algebra and Its Applications, 2011, 434(5): 1238-1254.

DOI：10.1016/j.laa.2010.11.005

• Cartan-Dieudonne
• Orthogonal matrices
• Householder transformations
• Orthogonal group
• Clifford algebras

We present an algorithmic proof of the Cartan-Dieudonne 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-Dieudonne-Scherk theorem is also discussed in relation to the minimum number of reflections required to decompose a given orthogonal transformation.

• 出版日期2011-3-1