A complex Hadamard matrix is any complex N × N {\displaystyle N\times N} matrix H {\displaystyle H} satisfying two conditions: unimodularity (the modulus...

In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose...

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...

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...

The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when...

multiplication also exist, such as the Hadamard product and the Kronecker product. They arise in solving matrix equations such as the Sylvester equation...

those with orthogonal columns, are called Hadamard matrices. More generally, suppose that N is a complex matrix of order n, whose entries are bounded by...

{\displaystyle \mathbf {x} .} More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if...

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...

{\mathit {K}}} form a Hadamard exponent. Thus, x K {\displaystyle {\mathit {xK}}} is the standard form of some complex Hadamard matrix H {\displaystyle {\mathit...

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...

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...

Hadamard may refer to: Zélie Hadamard (1849–1901), French actress Jacques Hadamard (1865–1963), a French mathematician, whose name is associated with the...

{\displaystyle \circ } represents the Hadamard product, and 1 is a constant vector with elements 1. The inverse matrix-to-vector diag operator is sometimes...

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

quantum sciences, such as SIC-POVMs, finite projective/affine planes, complex Hadamard matrices and more [see section: Related problems]. MUBs are important...

matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n × n real or complex matrix....

standard basis of complex sinusoids for eigenvectors of the Laplacian matrix of a graph corresponding to the signal. The Laplacian matrix is the easiest...

real numbers, complex numbers, or more generally elements of a field F. The trace is not defined for non-square matrices. Let A be a matrix, with A = (...

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...

Edge-of-the-wedge theorem Several complex variables Augustin Louis Cauchy Leonhard Euler Carl Friedrich Gauss Jacques Hadamard Kiyoshi Oka Bernhard Riemann...

matrix, from the usual O ( N 2 ) {\displaystyle O(N^{2})} . Similar techniques can be applied for multiplications by matrices such as Hadamard matrix...

function Hadamard code Hadamard's dynamical system Hadamard manifold Hadamard matrix Hadamard space Hadamard Transform and Hadamard gate Hadamard variance...

}=4+9+25+36=74.} Hadamard product (matrices) Hilbert–Schmidt inner product Kronecker product Matrix analysis Matrix multiplication Matrix norm Tensor product...

discrete-time systems. A matrix A is a Schur (stable) matrix if its eigenvalues are located in the open unit disk in the complex plane. Kharitonov region...

entries of a Hadamard product.) It can be shown that the total number of elementary multiplications L {\displaystyle L} required for matrix multiplication...

called interaction algorithm, which provided efficient computation of Hadamard and Walsh transforms. Yates' algorithm is still used in the field of statistical...

especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically...

in 1940, on January 28. Suppose that H is an n by n Hadamard matrix, where n=4ab. Then the matrix ( I a H / 2 H / 2 I b ) {\displaystyle...

quantum circuit consisting of only O ( n 2 ) {\displaystyle O(n^{2})} Hadamard gates and controlled phase shift gates, where n {\displaystyle n} is the...