Definition:Vandermonde Determinant/Formulation 1/Also presented as/Ones at Top

Definition

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

$V_n = \begin {vmatrix}

    1   &    1    & \cdots &  1 \\
  x_1   &  x_2    & \cdots &  x_n \\
{x_1}^2 & {x_2}^2 & \cdots & {x_n}^2 \\
 \vdots &  \vdots & \ddots & \vdots \\
{x_1}^{n - 2} & {x_2}^{n - 2} & \cdots & {x_n}^{n - 2} \\
{x_1}^{n - 1} & {x_2}^{n - 1} & \cdots & {x_n}^{n - 1}

\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

• 1994: H.E. Rose: A Course in Number Theory (2nd ed.) ... (previous) ... (next): Preface to first edition: Prerequisites: $\text {(i)}$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Vandermonde matrix