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Mathematics-Online course: Linear Algebra - Basic Structures - Bases

Linear Independence

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Vectors $ v_1,\dots,v_m$ in a $ K$-vector space are called linearly dependent, if there are $ \alpha_1,\dots,\alpha_m\in K$ so that

$\displaystyle \alpha_1 v_1 + \dots + \alpha_m v_m = 0 $

where at least one $ \alpha_i \neq 0$. Otherwise they are called linearly independent.

A subset $ M$ of $ V$ is called linearly independent, if any finite subset of $ M$ consists of linearly independent vectors. Otherwise $ M$ is said to be linearly dependent.

Abbreviations often used for linearly independentänd linearly dependentäre l. i.änd l. d.", resp.

(Authors: App/Burkhardt/Höllig/Kimmerle)

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  automatically generated 4/21/2005