Talk:Witt's theorem

Isometry

It is not needed that the bilinear form is symmetric!!! A "metric linear map" is an "isometry". Using both term is not helping for the understanding. The definition of an isometry is unclear. Try something like "An isometry of forms is an isomorphism of vector spaces which is also metric. Maybe for the references: Artin, Geometric Algebra. --Zuphilip 15:20, 25 June 2007 (UTC)[reply]

This article is using a generalized sense of isometry meaning a map that preserves a quadratic form, not necessarily positive definite. The actual isometry of this encyclopedia assumes a metric space context. Among experts this abuse of language is common, but for ordinary readers this usage of isometry may be confusing.Rgdboer (talk) 20:06, 26 April 2013 (UTC)[reply]

Now linked to Isometry (quadratic forms). Deltahedron (talk) 20:13, 26 April 2013 (UTC)[reply]

The section Statement of theorem still contains a link to the metric isometry article. Furthermore, it links to isometry group which again presumes a metric space.Rgdboer (talk) 21:02, 30 April 2013 (UTC)[reply]

Field characteristic

Hi, doesn't k need to have characteristic other than 2? 77.1.32.174 (talk) 17:01, 5 November 2011 (UTC)[reply]

Index is an invariant

"Witt's theorem implies that the dimension of a maximal totally isotropic subspace (null space) of V is an invariant …" -- I don't see why Witt's theorem should be needed for this statement. It is needed for the further claims of the quoted sentence, of course. — Preceding unsigned comment added by 178.203.174.18 (talk) 10:21, 26 May 2014 (UTC)[reply]

It's needed to show that this number is well defined: otherwise there might be maximal totally isotropic subspaces of different dimensions. The deduction is in Lam (2005). Deltahedron (talk) 15:39, 26 May 2014 (UTC)[reply]