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