Alternant (Linear Algebra)/Examples/Arbitrary Example 1

Example of Alternant in the context of Linear Algebra

An example of an alternant:

$\begin {vmatrix} 1 & 1 & 1 \\ x & y & z \\ x^2 & y^2 & z^2 \end {vmatrix}$

Here we have:

$r_1$, $r_2$ and $r_3$ are identified with $x$, $y$ and $z$

$f_1$ is identified with the constant mapping: $\map {f_1} {x_i} = 1$

$f_2$ is identified with the identity mapping: $\map {f_2} {x_i} = x_i$

$f_3$ is identified with the square function: $\map {f_3} {x_i} = {x_i}^2$