Mathematics-Online lexicon: Linear Map

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	Mathematics-Online lexicon:
	Linear Map

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overview

Let be -vector spaces. A map $\alpha: V \longmapsto W$ is called linear map, if for all $v_1,v_2,v \in V$ and $\lambda \in K$ the following holds true:

(i): $\alpha(v_1+v_2)=\alpha(v_1)+\alpha(v_2)$
(ii): $\alpha(\lambda v)=\lambda \alpha(v)$

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automatically generated 1/20/2005