Weighing Matrix (Paperback)

High Quality Content by WIKIPEDIA articles! In mathematics, a weighing matrix W of order n with weight w is an n x n (0,1, 1)-matrix such that WWT = wI. A weighing matrix is also called a weighing design. For convenience, a weighing matrix of order n and weight w is often denoted by W(n, w). A W(n, n 1) is equivalent to a conference matrix and a W(n, n) is an Hadamard matrix. Some properties are immediate from the definition: * The rows are pairwise orthogonal. * Each row and each column has exactly w non-zero elements. * WTW = wI, since the definition means that W 1 = w 1WT (assuming the weight is not 0). Example of W(2, 2): begin{pmatrix}-1 & 1 1 & 1end{pmatrix}