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Mathematics-Online lexicon:

Subspace

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A subset $ U$ of a $ K$-vector space $ V$ is called a vector subspace (or simply a subspace) of $ V$, if $ U$ itself, endowed with the addition and the scalar multiplication defined in $ V$, forms a vector space.

if $ u, v\in U$ and $ \lambda\in K$, then it immediatetly follows that $ u + v \in U $ and $ \lambda\cdot u \in U$.

(Authors: App/Burkhardt/Kimmerle)
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  automatically generated 4/ 1/2005