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Linear independence and dependence

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

Abstract

A set of vectors E is said to be linearly dependent if there exist distinct vectors A1,..., A k in E and numbers a1,...,a k , not all zero, such that
$$ {a_1}{{\rm{A}}_1}{\rm{ }} + {\rm{ }}{a_2}{{\rm{A}}_2}{\rm{ }} + {\rm{ }}...{\rm{ }} + {\rm{ }}{a_k}{{\rm{A}}_k} = 0. $$
(*)
Equation (*) is called a linear relation between A1,...,A k .

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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Larry Smith
    • 1
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany

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