Linear algebra MOC

Vandermonde matrix

A Vandermonde matrix 𝑇 ∈M𝑚,𝑛⁡(𝕂) is one of the form linalg

𝑇=⎡⎢ ⎢ ⎢⎣𝑥00…𝑥𝑛−10⋮⋱⋮𝑥0𝑚−1…𝑥𝑛−1𝑚−1⎤⎥ ⎥ ⎥⎦.

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

det𝑇=∏0≤𝑖<𝑗≤𝑛(𝑥𝑗−𝑥𝑖)

Proof

proof

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