翻訳と辞書 Words near each other ・ Maxwell Ward, 6th Viscount Bangor ・ Maxwell Wintrobe ・ Maxwell Woodhull House ・ Maxwell Woosnam (priest) ・ Maxwell Xolani Rani ・ Maxwell's ・ Maxwell's black weaver ・ Maxwell's demon ・ Maxwell's duiker ・ Maxwell's equations ・ Maxwell's equations in curved spacetime ・ Maxwell's Executors v. Wilkinson ・ Maxwell's Maniac ・ Maxwell's Plum ・ Maxwell's Silver Hammer ・ Maxwell's theorem ・ Maxwell's thermodynamic surface ・ Maxwell's Urban Hang Suite ・ Maxwell, California ・ Maxwell, Grey County, Ontario ・ Maxwell, Hastings County, Ontario ・ Maxwell, Indiana ・ Maxwell, Iowa ・ Maxwell, Morgan County, Indiana ・ Maxwell, Nebraska ・ Maxwell, New Mexico ・ Maxwell, New Zealand ・ Maxwell, Ontario ・ Maxwell, Texas ・ Maxwell-Bloch equations 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 Maxwell's theorem ： ウィキペディア英語版 Maxwell's theorem In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable ''X'' = ( ''X''1, ..., ''X''''n'' )''T'' is the same as the distribution of ''GX'' for every ''n''×''n'' orthogonal matrix ''G'' and the components are independent, then the components ''X''1, ..., ''X''''n'' are normally distributed with expected value 0, all have the same variance, and all are independent. This theorem is one of many characterizations of the normal distribution. Since a multiplication by an orthogonal matrix is a rotation, the theorem says that if the probability distribution of a random vector is unchanged by rotations and if the components are independent, then the components are identically distributed and normally distributed. In other words, the only rotationally invariant probability distributions on R''n'' that have independent components are multivariate normal distributions with expected value 0 and variance σ2''I''''n'', (where ''I''''n'' = the ''n''×''n'' identity matrix), for some positive number σ2. ==References== * * 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「Maxwell's theorem」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.