Inner Product Spaces

  • Frank Deutsch
Part of the CMS Books in Mathematics / Ouvrages de mathématiques de la SMC book series (CMSBM)


To motivate the subject matter of this book, we begin this chapter by listing five basic problems that arise in various applications of “least-squares” approximation. While these problems seem to be quite different on the surface, we will later see that the first three (respectively the fourth and fifth) are special cases of the general problem of best approximation in an inner product space by elements of a finite-dimensional subspace (respectively convex set). In this latter formulation, the problem has a rather simple geometric interpretation: A certain vector must be orthogonal to the linear subspace.


Hilbert Space Linear Space Product Space Cauchy Sequence Normed Linear Space 
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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Frank Deutsch
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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