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Mathematics-Online lexicon:

# Vector Space

 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

Let be a field. An Abelian group is called -vector space (vector space over ) if a scalar multiplication ,, is defined so that for all , , and for all , , the following holds true:

If or , then one speaks of a real or complex vectorspace, resp.

Note, that the plus stands for addition in and for addition in . The same stands for the multiplication.

(Authors: App/Burkhardt/Kimmerle)

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