Definition:Vandermonde Matrix/Formulation 2

Definition

The Vandermonde matrix of order $n$ is a square matrix specified variously as:

$\begin {bmatrix}

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 {bmatrix}$

That is, such that:

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

Also known as

A Vandermonde matrix is often seen referred to as Vandermonde's matrix.

The first form is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$ because it is slightly less grammatically unwieldy than the possessive style.

Also see

• Definition:Vandermonde Matrix/Formulation 1
• Definition:Vandermonde Determinant

• Results about Vandermonde matrices can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products: Exercises -- Second Set