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An algorithm for the Cartan-Dieudonné theorem on generalized scalar product spaces |
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| Authors: | M.A. Rodr?´ guez-Andrade,G. Aragó n-Gonzá lez |
| Affiliation: | a Departamento de Matemáticas, Escuela Superior de F?´sica y Matemáticas, IPN, México D.F. 07300, México and Departamento de Matemática Educativa Centro de Investigación y Estudios Avanzados, IPN, México D.F. 07360, Mexico b Programa de Desarrollo Profesional en Automatización, Universidad Autónoma Metropolitana, Azcapotzalco, San Pablo 180, Colonia Reynosa-Tamaulipas, México D.F. 02200, Mexico c Centro de F?´sica Aplicada y Tecnolog?´a Avanzada, Universidad Nacional Autónoma de México, Apartado 1-1010, Querétaro 76000, Mexico d Departamento de Matemáticas, Universidad Autónoma Metropolitana, Iztapalapa, Apartado 55-534, México D.F. 09340, Mexico |
| 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: | 15A23 15A30 15A66 |
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