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:...

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

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...

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

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

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...

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

_{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...

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

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

Toeplitz matrix, an "upside down" (that is, row-reversed) Hankel matrix Vandermonde matrix Yasuda, M. (2003). "A Spectral Characterization of Hermitian Centrosymmetric...

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}...

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

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

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...

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

variablesPages displaying wikidata descriptions as a fallback Vandermonde polynomial – determinant of Vandermonde matrixPages displaying wikidata descriptions as a...

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

fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally...

Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant matrix Hankel matrix...

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

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 =...

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...

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...

differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the...

of Alexandre-Théophile Vandermonde (1770) developed the theory of symmetric functions and solution of cyclotomic polynomials. Leopold Kronecker has been...

evaluation points were chosen suitably, this matrix is invertible (see also Vandermonde matrix), and so: ( r 0 r 1 r 2 r 3 r 4 ) = ( 1 0 0 0 0 1 1 1 1 1 1 −...

left-hand side matrix J T {\displaystyle \mathbf {J} ^{T}} is a transposed Vandermonde matrix, a rearrangement reveals that the coefficients are basically computed...