In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:...
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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...
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{\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...
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Polynomial interpolation (redirect from Vandermonde interpolation)
,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...
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et Métiers. Knight's Tour Knot theory Vandermonde's identity Vandermonde polynomial Vandermonde matrix Vandermonde : secret society of the Conservatoire...
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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...
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{\displaystyle \omega ^{x}=\omega ^{x{\bmod {N}}}.} This is the Vandermonde matrix for the roots of unity, up to the normalization factor. Note that...
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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...
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1950s). For example, a Vandermonde matrix whose nodes are positive and increasing is a totally positive matrix. Compound matrix George M. Phillips (2003)...
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< n which is required for the matrix to be invertible; then since X {\displaystyle \mathbf {X} } is a Vandermonde matrix, the invertibility condition is...
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Cauchy matrix Jacobi operator Toeplitz matrix, an "upside down" (that is, row-reversed) Hankel matrix Vandermonde matrix Yasuda, M. (2003). "A Spectral Characterization...
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{\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}}...
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\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...
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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...
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Determinant (redirect from Matrix determinant)
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...
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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...
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Triangular matrix Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant...
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List of named matrices (redirect from List of matrix)
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
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Projection matrix Jacobian matrix and determinant Scatter matrix Gram matrix Vandermonde matrix Everitt, B. S. (2002). Cambridge Dictionary of Statistics...
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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...
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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...
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Moore matrix, analogous to the Wrońskian with differentiation replaced by the Frobenius endomorphism over a finite field. Alternant matrix Vandermonde matrix...
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the general linear group over a finite field. Alternant matrix Vandermonde matrix Vandermonde determinant List of matrices Dickson, Leonard Eugene (1958)...
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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...
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normal equations matrix XTX is ill-conditioned. When fitting polynomials the normal equations matrix is a Vandermonde matrix. Vandermonde matrices become...
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Generalizations of Pauli matrices (redirect from Clock and shift matrix)
which is the desired analog result. Thus, W {\displaystyle W} , a Vandermonde matrix, arrays the eigenvectors of Σ 1 {\displaystyle \Sigma _{1}} , which...
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}^{\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}...
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that this form of the parity-check matrix, being composed of a Vandermonde matrix V {\displaystyle V} and diagonal matrix D {\displaystyle D} , shares the...
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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 ⋯...
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(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...
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