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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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## Recent Activity

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

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier

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

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier

## Comments

## Proof

any chance of getting a proof of this?

## Re: Proof

Proof has arrived!

## Re: Proof

Thanks.

Nice proof by the way!