Mathematics-Online lexicon: Dimensions of Kernel and Image

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	Mathematics-Online lexicon:
	Dimensions of Kernel and Image

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let $\alpha: V\longmapsto W$ be a linear map and let $\operatorname{dim} V<\infty$ . Then the following holds true:

(i): $\operatorname{Ker}(\alpha)$ is a subspace of .
(ii): $\operatorname{Im}(\alpha)$ is a subspace of .
(iii): $\operatorname{dim} V = \operatorname{dim}\operatorname{Ker}(\alpha) + \operatorname{dim}\operatorname{Im}(\alpha)$

Example:

automatically generated 6/25/2018