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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Centering matrix ： ウィキペディア英語版 Centering matrix In mathematics and multivariate statistics, the centering matrix〔John I. Marden, ''Analyzing and Modeling Rank Data'', Chapman & Hall, 1995, ISBN 0-412-99521-2, page 59.〕 is a symmetric and idempotent matrix, which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component. == Definition == The centering matrix of size ''n'' is defined as the ''n''-by-''n'' matrix :$C\_n\; =\; I\_n\; -\; \backslash tfrac\backslash mathbb$ where $I\_n\backslash ,$ is the identity matrix of size ''n'' and $\backslash mathbb$ is an ''n''-by-''n'' matrix of all 1's. This can also be written as: :$C\_n\; =\; I\_n\; -\; \backslash tfrac\backslash mathbf\backslash mathbf^\backslash top$ where $\backslash mathbf$ is the column-vector of ''n'' ones and where $\backslash top$ denotes matrix transpose. For example :$C\_1\; =\; \backslash begin$ 0 \end , :$C\_2=\; \backslash left(\backslash begin$ 1 & 0 \\ \\ 0 & 1 \end \right ) - \frac\left(\begin 1 & 1 \\ \\ 1 & 1 \end \right ) = \left(\begin \frac & -\frac \\ \\ -\frac & \frac \end \right ) , :$C\_3\; =\; \backslash left(\backslash begin$ 1 & 0 & 0 \\ \\ 0 & 1 & 0 \\ \\ 0 & 0 & 1 \end \right ) - \frac\left(\begin 1 & 1 & 1 \\ \\ 1 & 1 & 1 \\ \\ 1 & 1 & 1 \end \right ) = \left(\begin \frac & -\frac & -\frac \\ \\ -\frac & \frac & -\frac \\ \\ -\frac & -\frac & \frac \end \right ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Centering matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.