Vandermonde Determinant/Examples/Order 4

Example of Vandermonde Determinant

Consider the Vandermonde determinant of order $4$:

$V_n = \begin {vmatrix} 1 & 1 & 1 & 1 \\ x_1 & x_2 & x_3 & x_4 \\ {x_1}^2 & {x_2}^2 & {x_3}^2 & {x_4}^2 \\ {x_1}^3 & {x_2}^3 & {x_3}^3 & {x_4}^3 \end {vmatrix}$

Its value is:

$\paren {x_2 - x_1} \paren {x_3 - x_1} \paren {x_3 - x_2} \paren {x_4 - x_1} \paren {x_4 - x_2} \paren {x_4 - x_3}$

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Vandermonde matrix