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Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces of Finite Dimension

  • Ivan Singer
Chapter
  • 291 Downloads
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 171)

Abstract

An important particular case of best approximation in normed linear spaces E by elements of linear subspaces G is that when the dimension (real or complex, according to the space E) of G is finite: dim G = n < ∞. In this case*) G = [x 1,..., x n], where x 1,..., x n are linearly independent elements of G, and every element gG can be written, uniquely, in the form
$$g = \sum\limits_{k = 1}^n {\alpha _k x_k } $$
(1.1)
where α1,..., α n are scalars (real or complex, according to the space E); the linear combinations (1.1) are also called polynomials (in x 1,..., x n ).

Keywords

Banach Space Extremal Point Linear Subspace Compact Space Finite Dimension 
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 1970

Authors and Affiliations

  • Ivan Singer
    • 1
  1. 1.Institute of MathematicsAcademy of the Socialist Republic of RomaniaBucharestRomania

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