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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