In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose...
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mathematician Jacques Hadamard or German mathematician Issai Schur. The Hadamard product is associative and distributive. Unlike the matrix product, it is also...
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the sum of the entries of the Hadamard product Hadamard product of two matrices of the same size, resulting in a matrix of the same size, which is the...
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of Hadamard matrices where the rows are rearranged so that the number of sign changes in a row is in increasing order. In short, a Hadamard matrix is...
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2m × 2m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2m real numbers xn into 2m real numbers Xk. The Hadamard transform...
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A complex Hadamard matrix is any complex N × N {\displaystyle N\times N} matrix H {\displaystyle H} satisfying two conditions: unimodularity (the modulus...
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The Hadamard code is an error-correcting code named after Jacques Hadamard that is used for error detection and correction when transmitting messages over...
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recursive definition of the 2 m × 2 m {\displaystyle 2^{m}\times 2^{m}} Hadamard matrix H m {\displaystyle H_{m}} : H m = 1 2 ( H m − 1 H m − 1 H m − 1 − H...
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Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or −1. The...
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opposite of irregular matrix, a matrix with a different number of entries in each row Regular Hadamard matrix, a Hadamard matrix whose row and column sums...
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lengths of these vectors ||vi ||. Specifically, Hadamard's inequality states that if N is the matrix having columns vi, then | det ( N ) | ≤ ∏ i = 1 n...
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Paley construction (redirect from Jacobsthal matrix)
is a Hadamard matrix of size 2(q + 1). It is a symmetric Hadamard matrix. Applying Paley Construction I to the Jacobsthal matrix for GF(7), one...
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mathematics a regular Hadamard matrix is a Hadamard matrix whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a...
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Quantum logic gate (redirect from Hadamard operation)
Bloch sphere, and is therefore involutory. It is represented by the Hadamard matrix: H = 1 2 [ 1 1 1 − 1 ] . {\displaystyle H={\frac {1}{\sqrt...
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respect to this basis can be represented by the columns of a complex Hadamard matrix multiplied by a normalization factor. For d = 3 these matrices would...
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\circ } represents the Hadamard product and 1 {\displaystyle \mathbf {1} } is a constant vector with elements 1. The inverse matrix-to-vector diag {\displaystyle...
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matrix, from the usual O ( N 2 ) {\displaystyle O(N^{2})} . Similar techniques can be applied for multiplications by matrices such as Hadamard matrix...
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In mathematics, a complex Hadamard matrix H of size N with all its columns (rows) mutually orthogonal, belongs to the Butson-type H(q, N) if all its elements...
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Block design (section Hadamard 2-designs)
the m × m identity matrix. An Hadamard matrix can be put into standardized form (that is, converted to an equivalent Hadamard matrix) where the first row...
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multiplication also exist, such as the Hadamard product and the Kronecker product. They arise in solving matrix equations such as the Sylvester equation...
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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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The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform. The bit string...
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integrand with the help of the Hadamard lemma one can obtain the following useful expression for the derivative of the matrix exponent, ( d d t e X ( t )...
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{\displaystyle Trs} matrix using Hadamard product, (denoted by ∘ {\displaystyle \circ } ) of Tr matrix and n-dimensional Hadamard matrix whose rows (except...
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the m × m identity matrix. An Hadamard matrix can be put into standardized form (that is, converted to an equivalent Hadamard matrix) where the first row...
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function Hadamard code Hadamard's dynamical system Hadamard manifold Hadamard matrix Hadamard space Hadamard Transform and Hadamard gate Hadamard variance...
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In mathematics, the Hadamard product may refer to: Hadamard product of two matrices, the matrix such that each entry is the product of the corresponding...
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the determinant of W {\displaystyle W} . A weighing matrix is a generalization of Hadamard matrix, which does not allow zero entries. As two special cases...
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In mathematics, a symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number z T M z {\displaystyle z^{\operatorname...
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H-matrix can refer to various kinds of matrices denoted by the letter H: H-matrix, a matrix whose comparison matrix is an M-matrix Hadamard matrix, a square...
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