Mathematics-Online lexicon: Image and Kernel

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	Mathematics-Online lexicon:
	Image and Kernel

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

Given a linear map $\alpha: V\to W$ . The set

$\displaystyle \operatorname{Ker}(\alpha) := \{v \in V:\ \alpha(v) = 0\}$

is called kernel of $\alpha$ , and the set

$\displaystyle \operatorname{Im}(\alpha ) := \{w\in W:\ \exists v \in V\$ mit $\displaystyle \ \alpha(v)= w \}$

is called image of $\alpha$ .

(Authors: Burkhardt/W. Kimmerle)

see also:

automatically generated 3/15/2005