The Cartan-Dieudonné Theorem
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 , Dieudonné ). We also prove that every rotation in SO(n) is the composition of at most n flips (for n ≥ 3).
KeywordsOrthonormal Basis Rigid Motion Finite Dimension Positive Orientation Linear Isometry
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