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

{\displaystyle C(p)=V^{-1}\!DV} , where D is the diagonal matrix and V is the Vandermonde matrix corresponding to the λ's: D = [ λ 1 0 ⋯ 0 0 λ 2 ⋯ 0 0 0...

,a_{0})} of the above matrix equation X ⋅ A = Y {\displaystyle X\cdot A=Y} . The matrix X on the left is a Vandermonde matrix, whose determinant is known...

et Métiers. Knight's Tour Knot theory Vandermonde's identity Vandermonde polynomial Vandermonde matrix Vandermonde : secret society of the Conservatoire...

also be seen from the invertibility of the Vandermonde matrix, due to the non-vanishing of the Vandermonde determinant. But, as can be seen from the construction...

opposite signs.) It is also called the Vandermonde determinant, as it is the determinant of the Vandermonde matrix. The value depends on the order of the...

{\displaystyle \omega ^{x}=\omega ^{x{\bmod {N}}}.} This is the Vandermonde matrix for the roots of unity, up to the normalization factor. Note that...

1950s). For example, a Vandermonde matrix whose nodes are positive and increasing is a totally positive matrix. Compound matrix George M. Phillips (2003)...

and solving for them as below just amounts to the inversion of the Vandermonde matrix of these 4 eigenvalues.) Sum all such terms, here four such, e A t...

Cauchy matrix Jacobi operator Toeplitz matrix, an "upside down" (that is, row-reversed) Hankel matrix Vandermonde matrix Yasuda, M. (2003). "A Spectral Characterization...

< n which is required for the matrix to be invertible; then since X {\displaystyle \mathbf {X} } is a Vandermonde matrix, the invertibility condition is...

{\displaystyle \alpha } . Let A {\displaystyle A} be the above DFT matrix, a Vandermonde matrix with entries A i j = α i j {\displaystyle A_{ij}=\alpha ^{ij}}...

\mathbf {a} (\omega _{p})]} is an M × p {\displaystyle M\times p} Vandermonde matrix of steering vectors a ( ω ) = [ 1 , e j ω , e j 2 ω , … , e j ( M...

Moore matrix, analogous to the Wrońskian with differentiation replaced by the Frobenius endomorphism over a finite field. Alternant matrix Vandermonde matrix...

the general linear group over a finite field. Alternant matrix Vandermonde matrix Vandermonde determinant List of matrices Dickson, Leonard Eugene (1958)...

useful 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...

Projection matrix Jacobian matrix and determinant Scatter matrix Gram matrix Vandermonde matrix Everitt, B. S. (2002). Cambridge Dictionary of Statistics...

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

In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to...

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

(Some authors use the transpose of the above matrix.) Examples of alternant matrices include Vandermonde matrices, for which f j ( α ) = α j − 1 {\displaystyle...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

the 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...

which is the desired analog result. Thus, W {\displaystyle W} , a Vandermonde matrix, arrays the eigenvectors of Σ 1 {\displaystyle \Sigma _{1}} , which...

by using an FPGA. The above Vandermonde matrix solution can be extended to triple parity, but for beyond a Cauchy matrix construction is required. The...

normal equations matrix XTX is ill-conditioned. When fitting polynomials the normal equations matrix is a Vandermonde matrix. Vandermonde matrices become...

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

In mathematics, a Cauchy matrix, named after Augustin-Louis Cauchy, is an m×n matrix with elements aij in the form a i j = 1 x i − y j ; x i − y j ≠ 0...

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

in 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 ⋯...