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Bases and Dimension

  • Thomas Banchoff
  • John Wermer
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let V be a vector space. Let Y1, ..., Y l , be a set of vectors in V. The span of this set of vectors is defined as the collection of all vectors Y in V of the form
$$ Y\;{\text{ = }}\;{s_1}{Y_1}\;{\text{ + }}\;{s_2}{Y_2}\;{\text{ + }}\; \cdots \;{\text{ + }}\;{s_l}{Y_l},\;\;\;\;\;{s_1}{\text{,}}\;...{\text{,}}\;{s_l}\; \in \;\mathbb{R}{\text{.}} $$
The span of Y1, ... , Y l , is denoted
$$ [{Y_1},\;...{\rm{,}}\;{Y_l}]. $$

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Thomas Banchoff
    • 1
  • John Wermer
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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