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...

mathematician Jacques Hadamard or German mathematician Issai Schur. The Hadamard product is associative and distributive. Unlike the matrix product, it is also...

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...

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

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...

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...

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

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...

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...

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...

the 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...

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...

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...

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...

In mathematics, a symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number x T M x {\displaystyle \mathbf {x} ^{\mathsf...

The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform. The bit string...

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

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...

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...

existence of (0,1)-matrices with given row and column sums Hadamard matrix, a square matrix of 1 and −1 coefficients with each pair of rows having matching...

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...

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...

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...

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

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

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

{\displaystyle Trs} matrix using Hadamard product, (denoted by ∘ {\displaystyle \circ } ) of Tr matrix and n-dimensional Hadamard matrix whose rows (except...

transformation. 1 n {\displaystyle {\frac {1}{\sqrt {n}}}} times a Hadamard matrix. In general, any operator in a Hilbert space that acts by permuting...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...