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nLab > Latest Changes: quadratic form

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2012

    started quadratic form

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

    I understand that a quadratic form is a function q:V→kq\colon V \to k such that q(tv)=t 2q(v)q(t v) = t^2 q(v), and v,w↦q(v+w)−q(v)−q(w)v, w \mapsto q(v + w) - q(v) - q(w) is bilinear. This agrees with your definition if 22 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

    I added word polarization.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2015

    added historical pointer at the beginning of the References

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeAug 22nd 2020

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

    diff, v24, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 25th 2023

    added pointer to:

    diff, v31, current

1 to 7 of 7

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