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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 16th 2012

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeJan 17th 2012
• (edited Jan 17th 2012)

I understand that a quadratic form is a function $q\colon V \to k$ such that $q(t v) = t^2 q(v)$, and $v, w \mapsto q(v + w) - q(v) - q(w)$ is bilinear. This agrees with your definition if $2$ is invertible, but in general one cannot reconstruct $\langle{,}\rangle$.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 17th 2012

Right, thanks. I said something to this extent, but it was a mess and it was wrong. I have fixed it now.

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeJan 17th 2012