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Linear Algebra pp 186-215 | Cite as

Inner product spaces

  • Werner Greub
Part of the Graduate Texts in Mathematics book series (GTM, volume 23)

Abstract

An inner product in a real vector space E is abilinear function (,) having the following properties:
  1. 1.

    Symmetry: (x, y) = (y, x).

     
  2. 2.

    Positive definiteness: (x, x)≧0, and (x, x) = 0 only for the vector x = 0.

     

Keywords

Orthonormal Basis Cross Product Product Space Division Algebra Finite Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • Werner Greub
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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