Properties
Using the Leibniz formula for the determinant,
where Sn denotes the set of permutations of, and sgn(σ) denotes the signature of the permutation σ, we can rewrite the Vandermonde determinant as
The Vandermonde polynomial (multiplied with the symmetric polynomials) generates all the alternating polynomials.
If m ≤ n, then the matrix V has maximum rank (m) if and only if all αi are distinct. A square Vandermonde matrix is thus invertible if and only if the αi are distinct; an explicit formula for the inverse is known.
Read more about this topic: Vandermonde Matrix
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