Linearkombinationen 2012 13: Unterschied zwischen den Versionen

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=Linearkombinationen=
 
=Linearkombinationen=
{{Definition|(Linearkombination)<br />Als Linearkombination der Vektoren <math>\vec{v_1}, \vec{v_2}, ... , \vec{v_n}</math> bezeichnet man den Vektor <math>\vec{x}=\lambda_1\cdot \vec{v_1}+ \lambda_2 \cdot \vec{v_2} + ... + \lambda_n \cdot \vec{v_n}= \sum_{i=1}^n \lambda_i \cdot \vec{v_i}</math> (mit <math>\lambda_1, \lambda_2, ... ,\lambda_n \in \mathbb{R}</math>).}}
+
{{Definition|(Linearkombination)<br />Als Linearkombination der Vektoren <math>\vec{v_1}, \vec{v_2}, ... , \vec{v_n}</math> bezeichnet man den Vektor<br /> <math>\vec{x}=\lambda_1\cdot \vec{v_1}+ \lambda_2 \cdot \vec{v_2} + ... + \lambda_n \cdot \vec{v_n}= \sum_{i=1}^n \lambda_i \cdot \vec{v_i}</math> (mit <math>\lambda_1, \lambda_2, ... ,\lambda_n \in \mathbb{R}</math>).}}
 
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[[Kategorie:Linalg]]
 
[[Kategorie:Linalg]]

Version vom 13. Dezember 2012, 00:07 Uhr

Darstellung von Vektoren mittels anderer Vektoren

Linearkombinationen

Definition


(Linearkombination)
Als Linearkombination der Vektoren \vec{v_1}, \vec{v_2}, ... , \vec{v_n} bezeichnet man den Vektor
\vec{x}=\lambda_1\cdot \vec{v_1}+ \lambda_2 \cdot \vec{v_2} + ... + \lambda_n \cdot \vec{v_n}= \sum_{i=1}^n \lambda_i \cdot \vec{v_i} (mit \lambda_1, \lambda_2, ... ,\lambda_n \in \mathbb{R}).