Vandermonde matrix
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High Quality Content by WIKIPEDIA articles! In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row. The determinant of a square Vandermonde matrix (where m=n) can be expressed as: det(V) = prod_{1le ijle n} (alpha_j-alpha_i). This is called the Vandermonde determinant or Vandermonde polynomial. It is sometimes called the discriminant, although many sources, including this article, refer to the discriminant as the square of this determinant. Note that the Vandermonde determinant is alternating in t...
High Quality Content by WIKIPEDIA articles! In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row. The determinant of a square Vandermonde matrix (where m=n) can be expressed as: det(V) = prod_{1le ijle n} (alpha_j-alpha_i). This is called the Vandermonde determinant or Vandermonde polynomial. It is sometimes called the discriminant, although many sources, including this article, refer to the discriminant as the square of this determinant. Note that the Vandermonde determinant is alternating in the entries, meaning that permuting the ?i by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the determinant. It thus depends on the order, while its square (the discriminant) does not depend on the order.
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