anallagmatic pavement | H-matrix

A Hadamard matrix is a type of square (-1, 1)-matrix invented by Sylvester under the name of anallagmatic pavement, 26 years before Hadamard considered them. In a Hadamard matrix, placing any two columns or rows side by side gives half the adjacent cells the same sign and half the other sign. When viewed as pavements, cells with 1s are colored black and those with -1s are colored white. Therefore, the n×n Hadamard matrix H_n must have n(n - 1)/2 white squares (-1s) and n(n + 1)/2 black squares (1s).

Hadamard design | Hadamard graph | Hadamard's maximum determinant problem | integer matrix | Paley class | Paley construction | Paley's theorem | Walsh function