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Quadratic Form

  1. Mar 7, 2006 #1
    "Let Q(v)=<v,v> be the quadratic form associated to a real or hermitian inner product space. ... "

    What's a quadratic form?
  2. jcsd
  3. Mar 7, 2006 #2


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  4. Mar 7, 2006 #3
    So it's LITERALLY <v,v>?
  5. Mar 7, 2006 #4


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    In my lineair algebra course, it was defined like this (for the real case):

    I suppose you know what a billineair map is.
    If there is such a billineair map [itex]b:E \times E \to \mathbb{R}[/itex], where E is an n-dimensional Euclidean space, then we can define a map [itex]q:E \to \mathbb{R}[/itex] as [itex]q\left( {\vec x} \right) = b\left( {\vec x,\vec x} \right)[/itex].

    We call this q the quadratic form, associated to the billineair map b.

    So in general, we have then:

    [tex]q\left( {\vec x} \right) = \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {a_{ij} x_i x_j } } [/tex]
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