2011 | OriginalPaper | Buchkapitel
The Cartan–Dieudonné Theorem
verfasst von : Jean Gallier
Erschienen in: Geometric Methods and Applications
Verlag: Springer New York
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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 8.1). This important result is a special case of the “Cartan–Dieudonn’e theorem” (Cartan [4], Dieudonn’e [6]). We also prove that every rotation in SO(n) is the composition of at most n flips (for n ≥ 3).