Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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

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