| 翻訳と辞書 |
| gyrovector space ： ウィキペディア英語版 |
gyrovector space
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.〔Abraham A. Ungar (2005), "Analytic Hyperbolic Geometry: Mathematical Foundations and Applications", Published by World Scientific, ISBN 981-256-457-8, ISBN 978-981-256-457-3〕 Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups. Ungar developed his concept as a tool for the formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts - "boosts" are aspects of relative velocities, and should not be conflated with "translations"). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity.
== Name ==
Gyrogroups are weakly-associative-grouplike-structure. Ungar proposed the term gyrogroup was for what he called a gyrocommutative-gyrogroup with the term gyrogroup being reserved for the non-gyrocommutative case in analogy with groups vs commutative-groups. Gyrogroups are a type of Bol loop. Gyrocommutative gyrogroups are equivalent to ''K-loops''〔Hubert Kiechle (2002), "Theory of K-loops",Published by Springer,ISBN 3-540-43262-0, ISBN 978-3-540-43262-3〕 although defined differently. The terms ''Bruck loop''〔Larissa Sbitneva (2001), (Nonassociative Geometry of Special Relativity ), International Journal of Theoretical Physics, Springer, Vol.40, No.1 / Jan 2001〕 and ''dyadic symset''〔J lawson Y Lim (2004), (Means on dyadic symmetrie sets and polar decompositions ), Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Springer, Vol.74, No.1 / Dec 2004〕 are also in use.
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「gyrovector 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.
|
|