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・ Generalized mean
・ Generalized method of moments
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・ Generalized minimum-distance decoding
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Generalized permutation matrix
・ Generalized Petersen graph
・ Generalized phrase structure grammar
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Generalized permutation matrix : ウィキペディア英語版
Generalized permutation matrix
In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is
:\begin
0 & 0 & 3 & 0\\
0 & -2 & 0 & 0\\
1 & 0 & 0 & 0\\
0 & 0 & 0 & 1\end.
== Structure ==
An invertible matrix ''A'' is a generalized permutation matrix if and only if it can be written as a product of an invertible diagonal matrix ''D'' and an (implicitly invertible) permutation matrix ''P'': i.e.,
: A=DP.

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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