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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 overview

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:


[Annotations]

  automatically generated 3/15/2005