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Mathematics-Online lexicon:

Linear Map

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Let $ V,W$ be $ K$-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:

$ \alpha(v_1+v_2)=\alpha(v_1)+\alpha(v_2)$
$ \alpha(\lambda v)=\lambda \alpha(v)$


  automatically generated 1/20/2005