Definition:Vandermonde Determinant/Formulation 2

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

• Value of Vandermonde Determinant

• Results about the Vandermonde determinant can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.

Sources

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