In algebra, the Vandermonde polynomial of an ordered set of n variables X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} , named after Alexandre-Théophile...

In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:...

S2CID 122300795. Higham, N. J. (1988). "Fast Solution of Vandermonde-Like Systems Involving Orthogonal Polynomials". IMA Journal of Numerical Analysis. 8 (4): 473–486...

the Vandermonde polynomial and a symmetric polynomial, and form a quadratic extension of the ring of symmetric polynomials: the Vandermonde polynomial is...

alternating, and a polynomial since all alternating polynomials are divisible by the Vandermonde determinant. The degree d Schur polynomials in n variables...

Vandermonde polynomial is a polynomial. Schur polynomials are defined in this way, as an alternating polynomial divided by the Vandermonde polynomial...

our interpolation polynomial L ( x ) = ∑ j = 0 k x j m j {\textstyle L(x)=\sum _{j=0}^{k}x^{j}m_{j}} , we must invert the Vandermonde matrix ( x i ) j...

solution of cyclotomic polynomials; this paper anticipated later Galois theory (see also abstract algebra for the role of Vandermonde in the genesis of group...

_{i\neq j}(r_{i}-r_{j}).} It is thus the square of the Vandermonde polynomial times a n 2 n − 2 {\displaystyle a_{n}^{2n-2}} . This expression...

In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients: ( m + n r ) = ∑ k = 0 r (...

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...

Using a standard monomial basis for our interpolation polynomial we get the very complicated Vandermonde matrix. By choosing another basis, the Newton basis...

q-difference polynomial Quantum calculus LLT polynomial q-binomial coefficient q-Pochhammer symbol q-Vandermonde identity q-Bessel polynomials q-Charlier...

Specialized forms of Reed–Solomon codes, specifically Cauchy-RS and Vandermonde-RS, can be used to overcome the unreliable nature of data transmission...

well-defined and equivalent. Proof 2 An alternative proof uses the Vandermonde polynomial P ( x 1 , … , x n ) = ∏ i < j ( x i − x j ) . {\displaystyle P(x_{1}...

that has the coefficients of the interpolation polynomial as unknown variables and a confluent Vandermonde matrix as its matrix. The general methods of...

{\displaystyle \sum _{k=1}^{n}k^{p}=1^{p}+2^{p}+3^{p}+\cdots +n^{p}} as a polynomial in n {\displaystyle n} . In modern notation, Faulhaber's formula is ∑...

In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...

corresponds to the fact that the Euler characteristic of the circle is 0. Vandermonde polynomial Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin...

117–127 Δ {\displaystyle \Delta } is closely related to the Vandermonde polynomial. The polynomial x 3 + x + 1 {\displaystyle x^{3}+x+1} with discriminant...

Quasisymmetric function Ring of symmetric functions Symmetrization Vandermonde polynomial F. N. David, M. G. Kendall & D. E. Barton (1966) Symmetric Function...

}^{\mathbf {T} }{\mathbf {y} },} where J {\displaystyle \mathbf {J} } is a Vandermonde matrix, that is i {\displaystyle i} -th row of J {\displaystyle \mathbf...

Reed–Solomon codes, with code words constructed over a finite field using a Vandermonde matrix. Most practical erasure codes are systematic codes -- each one...

factorial, falling sequential product, or lower factorial) is defined as the polynomial ( x ) n = x n _ = x ( x − 1 ) ( x − 2 ) ⋯ ( x − n + 1 ) ⏞ n  factors =...

linear systems of the Vandermonde type. Press, William; Saul Teukolsky; William Vetterling; Brian Flannery (1992). "§3.1 Polynomial Interpolation and Extrapolation...

a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a Galois field). BCH codes were invented...

for computing the determinants of highly symmetric matrix such as the Vandermonde matrix | 1 1 1 ⋯ 1 x 1 x 2 x 3 ⋯ x n x 1 2 x 2 2 x 3 2 ⋯ x n 2 ⋮ ⋮ ⋮...

the above discussion, the DFT can be expressed as the DFT matrix, a Vandermonde matrix, introduced by Sylvester in 1867, F = [ ω N 0 ⋅ 0 ω N 0 ⋅ 1 ⋯...

this result to Taylor's theorem. Historically, this, as well as the Chu–Vandermonde identity, ( x + y ) n = ∑ k = 0 n ( n k ) ( x ) n − k ( y ) k , {\displaystyle...

mathematical theory of knots was first developed in 1771 by Alexandre-Théophile Vandermonde who explicitly noted the importance of topological features when discussing...