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Quadratic Forms

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Part of the Problem Books in Mathematics book series (PBM)

Abstract

A quadratic form q on E is a map of the form
$$x \to q\left( x \right) = P\left( {x,x} \right)$$
where P is a symmetric bilinear form over E; such a P is well determined by q by the formula
$$P\left( {x,y} \right) = \frac{1}{2}\left( {q\left( {x + y} \right) - q\left( x \right) - \left( y \right)} \right),$$
and is called the polar form of q. Over a subspace F of E, the restriction of q is still a quadratic form, denoted by q| F .

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Copyright information

© Marcel Berger 1984

Authors and Affiliations

  1. 1.U.E.R. de Mathematique et InformatiqueUniversité Paris VIIParis, Cedex 05France
  2. 2.Centre National de la Recherche ScientifiqueParisFrance
  3. 3.P.U.K.GrenobleFrance

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