Cartan–Dieudonné theorem

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In mathematics, the Cartan–Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, is a theorem on the structure of the automorphism group of symmetric bilinear spaces.

Statement of the theorem[edit]

Let (V, b) be an n-dimensional, non-degenerate symmetric bilinear space over a field with characteristic not equal to 2. Then, every element of the orthogonal group O(V, b) is a composition of at most n reflections.

See also[edit]