Talk:Symmetric bilinear form

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I am confused here. It would be interesting to talk about the isometries here of a symmetric bilinear form and the fact that they are all composed out of mirroring around hyperplanes, but the thing that stops me is the name mostly, orthogonal group, is that the group fixing the quadric defined by the form (thus roughly speaking : preserving the symmetric bilinear form up to scalar multiplication) or really preserving the actual symmetric bilinear form?? —The preceding unsigned comment was added by Evilbu (talk • contribs) 20:08, 17 February 2006 (UTC)

The orthogonal group is the group fixing the actual symmetric bilinear form. -- Fropuff 22:29, 17 February 2006 (UTC)

Hmm if I would like to explain a bit about isometries and how mirroring them over any field (char not two) generates them, i'd better do that here that article seems to take a whole other approach? Evilbu 22:51, 17 February 2006 (UTC)