In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal.

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them.

There is a vast literature on Hadamard matrices and their applications such as in error correcting codes (Hadamard codes), telecommunications (CDMA Walsh codes), statistics (Plackett-Burman designs).

Hadamard matrices # A Hadamard matrix is an n × n matrix H whose entries are either + 1 or 1 and whose rows are mutually orthogonal. For example, the matrix H 2 defined by (1 1 1 1) is a Hadamard …

The Hadamard conjecture (possibly due to Paley) states that a Hadamard matrix of order n exists if and only if n = 1, 2 or n is a multiple of 4. The module below implements constructions of Hadamard and …

Any Sylvester matrix of square order is equivalent to a symmetric matrix with constant row sum, and thus gives rise to such designs; these can be constructed using quadratic forms on a vector space …

An n × n matrix H is a Hadamard matrix if its entries are and its rows are orthogonal. Equivalently, its entries are ±1 and HHt ±1 = nI. In particular, det H = ±nn/2 . (1)

Use the geometric meaning of the determinant (volume of the paralellopiped spanned by the rows).

Foreword This is an introduction to the Hadamard matrices, focusing on the complex case, and geometric and analytic aspects. We discuss the Hadamard conjecture, and then the complex case, …

It follows that H>H = nI for every Hadamard matrix of order n. Also note that modifying a Hadamard matrix by multiplying a row/column by -1 or permuting the rows/columns yields another Hadamard …