Inner Product of Vectors. Norm

  • J. L. Nowinski
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 22)


The incorporation of a metric into the axiomatic system of affine spaces depends on the method chosen for evaluating the magnitude of arbitrarily directed vectors. The procedure universally adopted was probably suggested by Grassman and Gibbs. It consists of deriving the notion of length, or norm, of vectors from the concept of the inner (also called scalar, or dot) product of vectors. We shall subsequently denote the inner product of two vectors, x and y say, by the symbol (x, y) instead of the usual notation x · y. As we shall see later, this convention makes the transition from Euclidean to abstract spaces simpler and more natural.


Orthogonal Projection Axiomatic System Zero Vector Affine Space Usual Notation 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • J. L. Nowinski
    • 1
  1. 1.University of DelawareNewarkUSA

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