翻訳と辞書 Words near each other ・ Pseudo-Chalkidian vase painting ・ Pseudo-City ・ Pseudo-cold front ・ Pseudo-Crato ・ Pseudo-Cushing's syndrome ・ Pseudo-deltoidal icositetrahedron ・ Pseudo-Democritus ・ Pseudo-Demosthenes ・ Pseudo-determinant ・ Pseudo-differential operator ・ Pseudo-Dionysius the Areopagite ・ Pseudo-documentary ・ Pseudo-Dorotheos of Monemvasia ・ Pseudo-Dorotheus ・ Pseudo-Epiphanios ・ Pseudo-Euclidean space ・ Pseudo-Ezekiel ・ Pseudo-finite field ・ Pseudo-Geber ・ Pseudo-Gregory ・ Pseudo-Hadamard transform ・ Pseudo-Hegesippus ・ Pseudo-Hurler polydystrophy ・ Pseudo-Ingulf ・ Pseudo-intersection ・ Pseudo-Isidorian Decretals ・ Pseudo-Jerome ・ Pseudo-John ・ Pseudo-Kufic ・ Pseudo-Linus 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 Pseudo-Euclidean space ： ウィキペディア英語版 Pseudo-Euclidean space In mathematics and theoretical physics, a pseudo-Euclidean space is a finite-dimensional together with a non-degenerate indefinite quadratic form . Such a quadratic form can, given a suitable choice of basis , be applied to a vector , giving (with ) : $q(x)\; =\; \backslash left(x\_1^2+\backslash cdots\; +\; x\_k^2\backslash right)-\backslash left(x\_^2+\backslash cdots\; +\; x\_n^2\backslash right)$ which is called the ''magnitude'' of the vector . For true Euclidean spaces, , implying that the quadratic form is positive-definite rather than indefinite. Otherwise is an isotropic quadratic form. Note that if and , then , so that is a null vector. In a pseudo-Euclidean space, unlike in a Euclidean space, there exist vectors with negative magnitude. As with the term ''Euclidean space'', ''pseudo-Euclidean space'' may refer to either an affine space or a vector space (see point–vector distinction) over real numbers. == Geometry == The geometry of a pseudo-Euclidean space is consistent in spite of a breakdown of the some properties of Euclidean space; most notably that it is not a metric space as explained below. Though, its affine structure provides that concepts of line, plane and, generally, of an affine subspace (flat), can be used without modifications, as well as line segments. 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「Pseudo-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.