翻訳と辞書 Words near each other ・ Dual wield ・ Dual Work Exchanger Energy Recovery ・ Dual! Parallel Trouble Adventure ・ Dual-Axis Radiographic Hydrodynamic Test Facility ・ Dual-band blade antenna ・ Dual-beta ・ Dual-career commuter couples ・ Dual-clutch transmission ・ Dual-coding theory ・ Dual-control modes of ventilation ・ Dual-covenant theology ・ Dual-energy X-ray absorptiometry ・ Dual Analog Controller ・ Dual ball joint suspension ・ Dual basis ・ Dual basis in a field extension ・ Dual Blades ・ Dual board ・ Dual Box ・ Dual brain theory ・ Dual bundle ・ Dual carbon battery ・ Dual carriageway ・ Dual chartering ・ Dual City Sessions ・ Dual code ・ Dual Committee ・ Dual cone and polar cone ・ Dual consciousness ・ Dual consciousness (neuroscience) 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 Dual basis in a field extension ： ウィキペディア英語版 Dual basis in a field extension In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension ''L''/''K'', by using the field trace. This requires the property that the field trace ''Tr''''L''/''K'' provides a non-degenerate quadratic form over ''K''. This can be guaranteed if the extension is separable; it is automatically true if ''K'' is a perfect field, and hence in the cases where ''K'' is finite, or of characteristic zero. A dual basis is not a concrete basis like the polynomial basis or the normal basis; rather it provides a way of using a second basis for computations. Consider two bases for elements in a finite field, GF(''p''''m''): :$B\_1\; =\; \}$ then ''B''2 can be considered a dual basis of ''B''1 provided : Here the trace of a value in GF(''p''''m'') can be calculated as follows: :$\backslash operatorname(\backslash beta\; )\; =\; \backslash sum\_^\; \backslash beta^$ Using a dual basis can provide a way to easily communicate between devices that use different bases, rather than having to explicitly convert between bases using the change of bases formula. Furthermore, if a dual basis is implemented then conversion from an element in the original basis to the dual basis can be accomplished with a multiplication by the multiplicative identity (usually 1). 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「Dual basis in a field extension」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.