Linear Algebra pp 186-215 | Cite as

Inner product spaces

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


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.



Orthonormal Basis Cross Product Product Space Division Algebra Finite Dimension 
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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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