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Mathematics-Online course: Linear Algebra - Matrices - Determinants

Oriented 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 4/21/2005