The Equivalence of Quadratic Forms

  • O. T. O’Meara
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 117)

Abstract

One of the major accomplishments in the theory of quadratic forms is the classification of the equivalence class of a quadratic form over arithmetic fields. We are ready to present this part of the theory. Roughly speaking it goes as follows: the global solution is completely described by local and archimedean solutions, the local solution involves the dimension, the discriminant, and an invariant called the Hasse symbol, the complex archimedean solution is trivial, and the real archimedean solution is the well-known law of inertia of Sylvester.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • O. T. O’Meara
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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