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

Definition

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

$\begin {bmatrix}

 1 &  1  & \cdots  &   1 \\

x_1 & x_2 & \cdots & x_n \\ \vdots & \vdots & \cdots & \vdots \\ {x_1}^{n - 1} & {x_2}^{n - 1} & \cdots & {x_n}^{n - 1} \\ \end {bmatrix}$

That is, such that:

$a_{i j} = {x_j}^{i - 1}$

Also see

• Results about Vandermonde matrices can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.

Sources

• 1992: Roderick Gow: Cauchy's matrix, the Vandermonde matrix and polynomial interpolation (Bull. Irish Math. Soc. Vol. 28: pp. 45 – 52)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Vandermonde matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Vandermonde matrix