Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416874 | Linear Algebra and its Applications | 2011 | 17 Pages |
Abstract
We present an algorithmic proof of the 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M.A. Rodrı´guez-Andrade, G. Aragón-González, J.L. Aragón, Luis Verde-Star,