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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 affine combination ： ウィキペディア英語版 affine combination In mathematics, an affine combination of vectors ''x''1, ..., ''x''''n'' is a vector :$\backslash sum\_^\}\; =\; \backslash alpha\_\; x\_\; +\; \backslash alpha\_\; x\_\; +\; \backslash cdots\; +\backslash alpha\_\; x\_,$ called a linear combination of ''x''1, ..., ''x''''n'', in which the sum of the coefficients is 1, thus: :$\backslash sum\_^$ are scalars in ''K''. This concept is important, for example, in Euclidean geometry. The act of taking an affine combination commutes with any affine transformation ''T'' in the sense that :$T\backslash sum\_^\}\; =\; \backslash sum\_^\}$ In particular, any affine combination of the fixed points of a given affine transformation $T$ is also a fixed point of $T$, so the set of fixed points of $T$ forms an affine subspace (in 3D: a line or a plane, and the trivial cases, a point or the whole space). When a stochastic matrix, A, acts on a column vector, B, the result is a column vector whose entries are affine combinations of B with coefficients from the rows in A. ==See also== 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「affine combination」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.