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Mathematics-Online lexicon:

Dimensions of Kernel and Image

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Let $ \alpha: V\longmapsto W$ be a linear map and let $ \operatorname{dim} V<\infty$. Then the following holds true:
$ \operatorname{Ker}(\alpha)$ is a subspace of $ V$.
$ \operatorname{Im}(\alpha)$ is a subspace of $ W$.
$ \operatorname{dim} V =
\operatorname{dim}\operatorname{Ker}(\alpha) +


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  automatically generated 6/25/2018