Search results
Results from the WOW.Com Content Network
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
Frobenius inner product, the dot product of matrices considered as vectors, or, equivalently 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 product entry-by-entry; Kronecker product or tensor product, the generalization to any size of the ...
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix.This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
Hadamard product of two matrices, the matrix such that each entry is the product of the corresponding entries of the input matrices; Hadamard product of two power series, the power series whose coefficients are the product of the corresponding coefficients of the input series; a product involved in the Hadamard factorization theorem for entire ...
first case is called the Hadamard code while the second is called the augmented Hadamard code. The Hadamard code is unique in that each non-zero codeword has a Hamming weight of exactly , which implies that the distance of the code is also . In standard coding theory notation for block codes, the Hadamard code is a -code, that is, it
The proof of the nonexistence of Hadamard matrices with dimensions other than 1, 2, or a multiple of 4 follows: If >, then there is at least one scalar product of 2 rows which has to be 0. The scalar product is a sum of n values each of which is either 1 or −1, therefore the sum is odd for odd n, so n must be even.
Compatibility with Hadamard products [ edit ] Vectorization is an algebra homomorphism from the space of n × n matrices with the Hadamard (entrywise) product to C n 2 with its Hadamard product: vec ( A ∘ B ) = vec ( A ) ∘ vec ( B ) . {\displaystyle \operatorname {vec} (A\circ B)=\operatorname {vec} (A)\circ \operatorname {vec ...
The article (both title and content) suggests that the name "Hadamard product" is only used for matrices. However, a similar element-wise/entrywise product could be applied to vectors, or to multilinear tensors (multidimensional arrays), not just to the specific case of matrices (two-dimensional arrays).