Mathematics-Online lexicon: Determinant as Volume

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	Mathematics-Online lexicon:
	Determinant as Volume

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

The absolute value of the determinant of a real matrix

coincides with the

-dimensional volume of the parallelepiped spanned by the colums

$\displaystyle \vert\operatorname{det}A\vert = \operatorname{vol}\{\sum_{i=1}^n \alpha_i a_i:\ 0\le\alpha_i\le 1\}\, .$

(Authors: Burkhardt/Höllig/Hörner)

Example:

automatically generated 1/27/2005