Talk:Cartan–Dieudonné theorem

Naming
I think this theorem is named after Élie Cartan and not his son Henri Cartan but I am not perfectly sure. Can anyone confirm this ? MathMartin 11:38, 12 February 2006 (UTC)


 * I can confirm that. Artin in Geometric Algebra (New York 1957) specifically says it is due to E.Cartan and J.Dieudonné.13:42, 19 April 2007 (UTC)

Exceptional case
Does anyone have a reference that discusses the unique exception to this thereom in characteristic 2? -- Fropuff 19:03, 22 March 2006 (UTC)

The problem is that vector spaces over char 2 base fields admit no reflections, so the theorem fails for boring reasons. Here's one way of seeing this: take F to be characteristic 2 and let V = F^n. If f is a proper reflection then there exists some basis in which it acts as (x_1, ..., x_k, x_(k+1) ..., x_n) -> (-x_1, ..., -x_k, x_(k+1), ..., x_n) where k is odd. But x = -x in characteristic 2, so f is the identity, not a reflection--contradiction! A similar proof works for any vector space over a char 2 base field. PerVognsen 05:14, 6 June 2007 (UTC)