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Vandermonde Determinant

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The determinant of monomes $ 1,x,\ldots x^{n-1}$ evaluated at $ n$ points $ x_i$ equals

$\displaystyle \left\vert\begin{array}{cccc} 1 & x_1 & \ldots & x_1^{n-1} \\ ... ... & \ldots & x_n^{n-1} \end{array}\right\vert = \prod_{i>j} (x_i-x_j)\, . $

(Authors: Burkhardt/Höllig/Hörner)

Annotation:

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  automatically generated 1/27/2005