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Homedeterminant of the Vandermonde matrix

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# determinant of the Vandermonde matrix

Let $R$ 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

$\prod_{{1\leq i<j\leq n}}(a_{j}-a_{i}).$ |

Keywords:

Vandermonde-determinant

Synonym:

Vandermonde determinant

Type of Math Object:

Result

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

15A57*no label found*65F99

*no label found*65T50

*no label found*

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new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

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new image: information-theoretic-distributed-measurement-dds.png by rspuzio

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new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

## Comments

## Proof

any chance of getting a proof of this?

## Re: Proof

Proof has arrived!

## Re: Proof

Thanks.

Nice proof by the way!