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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted _[[quadratic form]]_

   started quadratic form

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeJan 17th 2012
   • (edited Jan 17th 2012)
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI 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 $\langle{,}\rangle$.

   I understand that a quadratic form is a function such that , and is bilinear. This agrees with your definition if is invertible, but in general one cannot reconstruct .

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 17th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexRight, thanks. I said something to this extent, but it was a mess and it was wrong. I have fixed it now.

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

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJan 17th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added word _polarization_.

   I added word polarization.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 10th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded historical pointer at the beginning of the [References](http://ncatlab.org/nlab/show/quadratic+form#References)

   added historical pointer at the beginning of the References

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeAug 22nd 2020
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexList the axioms entirely in terms of the quadratic form; generalize explicitly to quadratic maps between any two vector spaces. <a href="https://ncatlab.org/nlab/revision/diff/quadratic+form/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/quadratic+form/24">v24</a>, <a href="https://ncatlab.org/nlab/show/quadratic+form">current</a>

   List the axioms entirely in terms of the quadratic form; generalize explicitly to quadratic maps between any two vector spaces.

   diff, v24, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Richard Elman]], [[Nikita Karpenko]], [[Alexander Merkurjev]], *Algebraic and Geometric Theory of Quadratic Forms*, Colloquium Publication **56**, AMS (2008) &lbrack;[ams:coll-56](https://bookstore.ams.org/coll-56), [pdf](https://www.math.ucla.edu/~rse/old_book/Kniga.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quadratic+form/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/quadratic+form/31">v31</a>, <a href="https://ncatlab.org/nlab/show/quadratic+form">current</a>

   added pointer to:

   • Richard Elman, Nikita Karpenko, Alexander Merkurjev, Algebraic and Geometric Theory of Quadratic Forms, Colloquium Publication 56, AMS (2008) [ams:coll-56, pdf]

   diff, v31, current