The SURVEYMEANS Procedure

Hadamard Matrix

A Hadamard matrix $\mb {H}$ is a square matrix whose elements are either 1 or –1 such that

\[  \mb {H}\mb {H}’=k\mb {I}  \]

where k is the dimension of $\mb {H}$ and $\mb {I}$ is the identity matrix of order k. The order k is necessarily 1, 2, or a positive integer that is a multiple of 4.

For example, the following matrix is a Hadamard matrix of dimension k = 8:

\[  \begin{array}{rrrrrrrr} 1 &  1 &  1 &  1 &  1 &  1 &  1 &  1\\ 1 &  -1 &  1 &  -1 &  1 &  -1 &  1 &  -1\\ 1 &  1 &  -1 &  -1 &  1 &  1 &  -1 &  -1\\ 1 &  -1 &  -1 &  1 &  1 &  -1 &  -1 &  1\\ 1 &  1 &  1 &  1 &  -1 &  -1 &  -1 &  -1\\ 1 &  -1 &  1 &  -1 &  -1 &  1 &  -1 &  1\\ 1 &  1 &  -1 &  -1 &  -1 &  -1 &  1 &  1\\ 1 &  -1 &  -1 &  1 &  -1 &  1 &  1 &  -1 \end{array}  \]