Weighing matrix
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In mathematics, a weighing matrix W of order n with weight w is an n × n (0,1, − 1)-matrix such that WWT = wI.
For convenience, a weighing matrix of order n and weight w is often denoted by W(n,w). A W(n,n − 1) is called a conference matrix and a W(n,n) is a Hadamard matrix.
Several properties can be immediately deduced: The rows are pairwise orthogonal, each row has exactly w non-zero elements, each column has exactly w non-zero elements.
The main question about weighing matrices is their existence: for which values of n and w does there exist a W(n,w)? A great deal about this is unkown. An equally important but often overlooked question about weighing matrices is their classification: for a given n and w, how many W(n,w)'s are there?
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