Classification of ⊥-Dense Subspaces with Definite Forms

  • Herbert Gross
Part of the Progress in Mathematics book series (PM, volume 1)


The fields k admitted in this chapter are the same as those of Chapter Twelve but with the additional proviso that kO is archimedean ordered. (E,Φ) will be a non degenerate hermitean space of dimension ℵO which is weakly universal and has 1 ∈ ‖Φ‖ . In contrast to Chapter Twelve the space (E,Φ) is not assumed to be positive definite.


Orthonormal Basis Standard Basis Orthogonal Group Dense Subspace Isotropic Subspace 


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References to Chapter XIII

  1. [1]
    E. Artin, Geometric Algebra, Interscience Publ. NY (1957).Google Scholar
  2. [2]
    F. van der Blij, History of the octaves in Simon Slevin, Wis-en Natuurkundig Tijdschrift (Groningen) 34e Jaargang Avlevering III Februari 1961.Google Scholar
  3. [3]
    W. Greub, Multilinear Algebra, Springer Verlag NY (1967).Google Scholar
  4. [4]
    H. Gross, Eine Bemerkung zu dichten Unterräumen reeller quadratischer Räume. Comment. Math. Helv. 45, 472–493 (1970).MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    T.Y. Lam, The Algebraic Theory of Quadratic Forms, Benjamin, Inc. Reading (Mass ) 1973.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Herbert Gross
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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