Mathematics-Online lexicon: Linear Combination

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	Mathematics-Online lexicon:
	Linear Combination

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Given vectors $v_1, v_2,\dots,v_m$ in a

-vector space and given $\lambda_i \in K$ . A sum of the form

$\displaystyle \lambda_1 v_1 + \lambda_2 v_2 +\dots + \lambda_m v_m = \sum_{i=1}^m \lambda_i v_i$

is called a linear combination of the vectors

More generally:

Let $W \subset V$ . A liner combination from is a linear combination of a finite number of vectors from , that is, it is a finite sum of the form

$\displaystyle \lambda_1 w_1 + \lambda_2 w_2 + \dots + \lambda_k w_k = \sum_{i=1}^k \lambda_i w_i \, ,$

where $w_i \in W$ and $\lambda_i \in K$ für $1 \leq i \leq k$ .

(Authors: App/Burkhardt/Kimmerle)

Example:

automatically generated 2/10/2005