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Mathematics-Online lexicon:

Determinant as Volume

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The absolute value of the determinant of a real matrix $ A$ coincides with the $ n$-dimensional volume of the parallelepiped spanned by the colums $ a_i$:

$\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)


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  automatically generated 1/27/2005