翻訳と辞書 Words near each other ・ Conjugate prior ・ Conjugate residual method ・ Conjugate transpose ・ Conjugate vaccine ・ Conjugate variables ・ Conjugate variables (thermodynamics) ・ Conjugate-permutable subgroup ・ Conjugated estrogen ・ Conjugated fatty acid ・ Conjugated linoleic acid ・ Conjugated microporous polymer ・ Conjugated protein ・ Conjugated system ・ Conjugation ・ Conjugation of auxiliary Catalan verbs ・ Conjugation of isometries in Euclidean space ・ Conjunct ・ Conjunct Consulting ・ Conjunctio ・ Conjunction ・ Conjunction (astronomy) ・ Conjunction (grammar) ・ Conjunction Arts ・ Conjunction elimination ・ Conjunction fallacy ・ Conjunction introduction ・ Conjunctions ・ Conjunctiva ・ Conjunctival concretion ・ Conjunctival squamous cell carcinoma Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Conjugation of isometries in Euclidean space ： ウィキペディア英語版 Conjugation of isometries in Euclidean space In a group, the conjugate by ''g'' of ''h'' is ''ghg''−1. ==Translation== If ''h'' is a translation, then its conjugate by an isometry can be described as applying the isometry to the translation: *the conjugate of a translation by a translation is the first translation *the conjugate of a translation by a rotation is a translation by a rotated translation vector *the conjugate of a translation by a reflection is a translation by a reflected translation vector Thus the conjugacy class within the Euclidean group ''E''(''n'') of a translation is the set of all translations by the same distance. The smallest subgroup of the Euclidean group containing all translations by a given distance is the set of ''all'' translations. Thus this is the conjugate closure of a singleton containing a translation. Thus ''E''(''n'') is a semidirect product of the orthogonal group ''O''(''n'') and the subgroup of translations ''T'', and ''O''(''n'') is isomorphic with the quotient group of ''E''(''n'') by ''T'': :''O''(''n'') $\backslash cong$ ''E''(''n'') ''/ T'' Thus there is a partition of the Euclidean group with in each subset one isometry that keeps the origin fixed, and its combination with all translations. Each isometry is given by an orthogonal matrix ''A'' in ''O''(''n'') and a vector ''b'': :$x\; \backslash mapsto\; Ax+\; b$ and each subset in the quotient group is given by the matrix ''A'' only. Similarly, for the special orthogonal group ''SO''(''n'') we have :''SO''(''n'') $\backslash cong$ ''E''+(''n'') ''/ T'' 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「Conjugation of isometries in Euclidean space」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.