Vandermonde matrix

A Vandermonde matrix $𝑇 \in M 𝑚, 𝑛 (𝕂)$ is one of the form #m/def/linalg

𝑇 = ⎡ ⎢ ⎢ ⎢ ⎣ 𝑥 00 \dots 𝑥 𝑛 - 1 0 ⋮ ⋱ ⋮ 𝑥 0 𝑚 - 1 \dots 𝑥 𝑛 - 1 𝑚 - 1 ⎤ ⎥ ⎥ ⎥ ⎦ .

For a square matrix (i.e. $𝑚 = 𝑛$ ), the Vandermonde determinant is given by

d e t 𝑇 = \prod 0 \leq 𝑖 < 𝑗 \leq 𝑛 (𝑥 𝑗 - 𝑥 𝑖)

Proof

#missing/proof

#state/tidy | #lang/en | #SemBr