In 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 multiple of 4, regular Hadamard matrices carry the further restriction that the order must be a square number. The excess, denoted E(H ), of a Hadamard matrix H of order n is defined to be the sum of the entries of H. The excess satisfies the bound
|E(H )| ≤ n3/2. A Hadamard matrix attains this bound if and only if it is regular.
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opposite of irregular matrix, a matrix with a different number of entries in each row RegularHadamardmatrix, a Hadamardmatrix whose row and column sums...
In mathematics, a Hadamardmatrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose...
{\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 Hadamardmatrix can be put into standardized form (that is, converted to an equivalent Hadamardmatrix) where the first row...
gate with respect to a Hadamard transformed basis { | + ⟩ , | − ⟩ } {\displaystyle \{|+\rangle ,|-\rangle \}} . The Hadamard transformed basis of a one-qubit...
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...
the m × m identity matrix. An Hadamardmatrix can be put into standardized form (that is, converted to an equivalent Hadamardmatrix) 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...
designs from each Hadamardmatrix is 23 choose 6; that is 100,947 designs from each 24×24 Hadamardmatrix. Since there are 60 Hadamard matrices of that...
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 (...
\mathbf {F} ={\begin{bmatrix}1&1\\1&-1\\\end{bmatrix}},} (which is a Hadamardmatrix) 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 Hadamardmatrix of order 4 k {\displaystyle 4k}...
diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: If U {\displaystyle U} , V {\displaystyle V} are connected...
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...
techniques generalising the well-known "method of descent" due to Jacques Hadamard. In particular Flensted-Jensen (1978) gave a general method for deducing...
to prove all of them but one [the Riemann Hypothesis itself]. — Jacques Hadamard, The Mathematician's Mind, VIII. Paradoxical Cases of Intuition Riemann's...
is generated by this subgroup and the block diagonal matrix H4⊕H4 where H4 is the Hadamardmatrix H 4 = 1 2 [ 1 1 1 1 1 − 1 1 − 1 1 1 − 1 − 1 1 − 1 − 1...
scalars and where pi(n) is a polynomial in n for all 1 ≤ i ≤ ℓ. In general, Hadamard products of rational functions produce rational generating functions. Similarly...
functions (or vectors of a Hadamardmatrix). The receiver again measures the amplitudes for all 64 vectors (here comes the Hadamard Transform) and chooses...
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