Cartan-Dieudonné theorem

Cartan-Dieudonné theorem

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.

tatement 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.

See also

* Orthogonal group

References

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


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