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,...

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...

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

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...

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

{\displaystyle k=1,2,\ldots .} J is the neutral element of the Hadamard product. When J is considered as a matrix over the real numbers, the following additional properties...

is constructed as the Hadamard product of the real symmetric matrix of the symmetrized Laplacian and the Hermitian phase matrix with the complex entries...

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...

corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse...

gate with respect to a Hadamard transformed basis { | + ⟩ , | − ⟩ } {\displaystyle \{|+\rangle ,|-\rangle \}} . The Hadamard transformed basis of a one-qubit...

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...

embedded in E3, the Gauss map provides an explicit diffeomorphism. As Hadamard observed, in this case the surface is convex; this criterion for convexity...

square Gray code Hadamard matrices Complex Hadamard matrices Butson-type Hadamard matrices Generalized Hadamard matrices Regular Hadamard matrices Hall's...

value of x. 2.  Hadamard product of matrices: If A and B are two matrices of the same size, then A ∘ B {\displaystyle A\circ B} is the matrix such that (...

designs from each Hadamard matrix is 23 choose 6; that is 100,947 designs from each 24×24 Hadamard matrix. Since there are 60 Hadamard matrices of that...

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...

\mathbf {F} ={\begin{bmatrix}1&1\\1&-1\\\end{bmatrix}},} (which is a Hadamard matrix) or when N = 4 {\displaystyle N=4} as in the Discrete Fourier transform...

ordinary differential equations. Hadamard conjecture: for every positive integer k {\displaystyle k} , a Hadamard matrix of order 4 k {\displaystyle 4k}...

to prove all of them but one [the Riemann Hypothesis itself]. — Jacques Hadamard, The Mathematician's Mind, VIII. Paradoxical Cases of Intuition Riemann's...

 J. A. (ed.). "Sequence A003432 (Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.)". The On-Line Encyclopedia...

Paley. They are closely related to the Paley construction for constructing Hadamard matrices from quadratic residues. They were introduced as graphs independently...

diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: If U {\displaystyle U} , V {\displaystyle V} are connected...

techniques generalising the well-known "method of descent" due to Jacques Hadamard. In particular Flensted-Jensen (1978) gave a general method for deducing...

by the fact that he worked so often by visual representation. Jacques Hadamard wrote that Poincaré's research demonstrated marvelous clarity and Poincaré...

is generated by this subgroup and the block diagonal matrix H4⊕H4 where H4 is the Hadamard matrix H 4 = 1 2 [ 1 1 1 1 1 − 1 1 − 1 1 1 − 1 − 1 1 − 1 − 1...

multiple OFDM subcarriers. But unlike MC-CDMA, which uses binary-phase Hadamard codes (code values of 0 or 180 degrees) or binary pseudonoise, CI codes...

generating functions. For example: Aitken's Array: Triangle of Numbers Hadamard products of generating functions and diagonal generating functions, and...

where I {\displaystyle I} is the identity matrix and H {\displaystyle H} is a 24 by 24 Hadamard matrix (Z/23Z ∪ ∞) with a = 2 and b = 3, and entries...

Dagger compact category Haim, Mariana (2007). "Group-like algebras and Hadamard matrices". J. Algebra. 308 (1): 215–235. arXiv:math/0602224. CiteSeerX 10...

Secrets of Triangles. Prometheus Books. p. 22. Jacobs 1974, pp. 384–393. Hadamard, Jacques (2008). Lessons in Geometry, Vol. I: Plane Geometry. American...