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Linear Algebra pp 216-245 | Cite as

Inner product spaces

  • Larry Smith
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

So far in our study of vector spaces and linear transformations we have made no use of the notions of length and angle, although these concepts play an important role in our intuition for the vector algebra of ℝ2 and ℝ3. In fact the length of a vector and the angle between two vectors play very important parts in the further development of linear algebra and it is now time to introduce these ingredients into our study. There are many ways to do this and in the approach that we will follow both length and angle will be derived from a more fundamental concept called a scalar or inner product of two vectors.

Keywords

Vector Space Scalar Product Linear Transformation Linear Subspace Product Space 
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. 1978

Authors and Affiliations

  • Larry Smith
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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