PlanetMath: determinant of the Vandermonde matrix

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determinant of the Vandermonde matrix

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Let be a commutative ring with identity, and fix elements $a_1,a_2,...,a_n \in R$ . The determinant of the Vandermonde matrix $\big((a_i)^{j-1}\big)_{i,j=1}^n$ is equal to the product

$\displaystyle \prod_{1 \leq i < j \leq n}(a_j - a_i).$

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"determinant of the Vandermonde matrix" is owned by GeraW. [ full author list (2) ]

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Keywords:

Vandermonde-determinant

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Attachments:: proof of determinant of the Vandermonde matrix (Proof) by rspuzio

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Cross-references: product, fix, identity, commutative ring
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This is version 6 of determinant of the Vandermonde matrix, born on 2004-08-31, modified 2006-06-10.
Object id is 6120, canonical name is DeterminantOfTheVandermondeMatrix.
Accessed 5182 times total.

Classification:

AMS MSC:	65T50 (Numerical analysis :: Numerical methods in Fourier analysis :: Discrete and fast Fourier transforms)
	65F99 (Numerical analysis :: Numerical linear algebra :: Miscellaneous)
	15A57 (Linear and multilinear algebra; matrix theory :: Other types of matrices )

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