Hadamard matrix
时间: 2023-10-09 07:17:07 浏览: 43
A Hadamard matrix is a square matrix H of size n × n, with entries either +1 or −1, such that the rows of H are mutually orthogonal and have the same magnitude. In other words, if we take any two rows of H and multiply them element-wise, the sum of the resulting products is either n or −n, depending on whether the rows are orthogonal or not. Hadamard matrices have many interesting properties and applications in various areas of mathematics, engineering, and computer science, such as signal processing, coding theory, and quantum computing. The construction of Hadamard matrices is a highly nontrivial problem, and only a few families of such matrices are known to exist. The most famous one is the Sylvester construction, which produces Hadamard matrices of size 2^k for any positive integer k.