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Weighing matrix : ウィキペディア英語版 | Weighing matrix
In mathematics, a weighing matrix ''W'' of order ''n'' and weight ''w'' is an ''n'' × ''n'' (0,1,-1)-matrix such that , where is the transpose of and is the identity matrix of order . For convenience, a weighing matrix of order ''n'' and weight ''w'' is often denoted by ''W''(''n'',''w''). A ''W''(''n'',''n'') is a Hadamard matrix and a ''W(n,n-1)'' is equivalent to a conference matrix. ==Properties==
Some properties are immediate from the definition. If ''W'' is a ''W''(''n'',''w''), then: * The rows of ''W'' are pairwise orthogonal (that is, every pair of rows you pick from ''W'' will be orthogonal). Similarly, the columns are pairwise orthogonal. * Each row and each column of ''W'' has exactly ''w'' non-zero elements. * , since the definition means that , where is the inverse of . * where is the determinant of .
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