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arXiv · 1011.1027

An algorithm for the Cartan-Dieudonn\'e theorem on generalized scalar product spaces

M. A. Rodríguez-Andrade·G. Aragón-González·J. L. Aragón·Luis Verde-Star
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Abstract

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

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M. A. Rodríguez-Andrade, G. Aragón-González, J. L. Aragón, Luis Verde-Star. 2010-11-03. An algorithm for the Cartan-Dieudonn\'e theorem on generalized scalar product spaces. https://doi.org/10.1016/j.laa.2010.11.005

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