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The Cartan-Dieudonné Theorem

  • Jean Gallier
Part of the Texts in Applied Mathematics book series (TAM, volume 38)

Abstract

In this chapter the structure of the orthogonal group is studied in more depth. In particular, we prove that every isometry in O(n) is the composition of at most n reflections about hyperplanes (for n ≥ 2, see Theorem 7.2.1). This important result is a special case of the “Cartan-Dieudonné theorem” (Cartan [29], Dieudonné [47]). We also prove that every rotation in SO(n) is the composition of at most n flips (for n ≥ 3).

Keywords

Orthonormal Basis Rigid Motion Finite Dimension Positive Orientation Linear Isometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Jean Gallier
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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