# Definition:Vandermonde Determinant/Formulation 2

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## Definition

The **Vandermonde determinant of order $n$** is the determinant defined as:

- $V_n = \begin {vmatrix} x_1 & {x_1}^2 & \cdots & {x_1}^n \\ x_2 & {x_2}^2 & \cdots & {x_2}^n \\ \vdots & \vdots & \ddots & \vdots \\ x_n & {x_n}^2 & \cdots & {x_n}^n \end{vmatrix}$

## Also presented as

The **Vandermonde determinant of order $n$** can be presented in various orientations, for example:

- $V_n = \begin {vmatrix} x_1 & x_2 & \cdots & x_n \\ {x_1}^2 & {x_2}^2 & \cdots & {x_n}^2 \\ \vdots & \vdots & \ddots & \vdots \\ {x_1}^n & {x_2}^n & \cdots & {x_n}^n \end{vmatrix}$

## Also see

- Results about
**the Vandermonde determinant**can be found**here**.

## Source of Name

This entry was named for Alexandre-ThÃ©ophile Vandermonde.

## Sources

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