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Composition of Linear Maps

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Given two linear maps $ \alpha: U \longmapsto V$ and $ \beta: V \longmapsto W$. The composition of this two maps $ \alpha$ and $ \beta$ (in this order) works as follows: An element $ u \in U$ is mapped by $ \alpha$ to an element in $ V$ which is mapped by $ \beta$ to an element in $ W$. Notation: $ \beta \circ \alpha$ (read: $ \beta$ ,,after`` $ \alpha$): The map $ \beta$ is used after the map $ \alpha$ has been applied. The composition of two linear maps is a linear map.

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  automatically generated 3/15/2005