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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 WW^=wI_n, where W^T is the transpose of W and I_n is the identity matrix of order n.
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.
* W^W=wI, since the definition means that W^ = w^W^, where W^ is the inverse of W.
* \operatorname(W)=\pm w^ where \operatorname(W) is the determinant of W.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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