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.

[edit] Statement of the theorem

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.

[edit] See also

• Orthogonal group

[edit] References

• Sylvestre Gallot, Dominique Hulin, Jacques LaFontaine, Riemannian Geometry, Springer, 2004. ISBN 3540204938.
• Jean H Gallier, Geometric Methods and Applications, Springer, 2000. ISBN 0387950443.