Linear Algebra pp 160-185 | Cite as

Inner product spaces

  • Werner H. Greub
Conference paper
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 97)


An inner product in a real linear space E is a bilinear function (x,y) having the following properties:
  1. 1.

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

  2. 2.

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



Linear Space Orthonormal Basis Product Space Bilinear Function Dual Basis 
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 Berlin Heidelberg 1963

Authors and Affiliations

  • Werner H. Greub
    • 1
  1. 1.Mathematics DepartmentUniversity of TorontoCanada

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