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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 Minkowski addition ： ウィキペディア英語版 Minkowski addition In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors ''A'' and ''B'' in Euclidean space is formed by adding each vector in ''A'' to each vector in ''B'', i.e., the set : $A\; +\; B\; =\; \backslash \backslash ,|\backslash ,\backslash mathbf\backslash in\; A,\backslash \; \backslash mathbf\backslash in\; B\backslash \}.$ Analogously, the Minkowski difference is defined as : $A\; -\; B\; =\; \backslash \backslash ,|\backslash ,\backslash mathbf\backslash in\; A,\backslash \; \backslash mathbf\backslash in\; B\backslash \}.$ The concept is named for Hermann Minkowski. ==Example== For example, if we have two sets ''A'' and ''B'', each consisting of three position vectors (informally, three points), representing the vertices of two triangles in $\backslash mathbb^2$, with coordinates : and :, then the Minkowski sum is , which looks like a hexagon, with three 'repeated' points at . For Minkowski addition, the ''zero set'' , containing only the zero vector 0, is an identity element: For every subset S, of a vector space : S +  = S; The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset, S, of a vector space, its sum with the empty set is empty: . 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「Minkowski addition」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.