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Duplication and elimination matrices : ウィキペディア英語版 | Duplication and elimination matrices In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa. ==Duplication matrix== The duplication matrix ''D''''n'' is the unique ''n''2 × ''n''(''n''+1)/2 matrix which, for any ''n'' × ''n'' symmetric matrix ''A'', transforms vech(''A'') into vec(''A''): :''D''n vech(''A'') = vec(''A''). For the 2×2 symmetric matrix ''A'' = , this transformation reads :
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