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.

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.

See also

• Indefinite orthogonal group
• Orthogonal group
• Coordinate rotations and reflections

References

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