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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rational dependence ： ウィキペディア英語版 Rational dependence In mathematics, a collection of real numbers is rationally independent if none of them can be written as a linear combination of the other numbers in the collection with rational coefficients. A collection of numbers which is not rationally independent is called rationally dependent. For instance we have the following example. :$$ \begin \mbox\qquad\\ \underbrace, 1+\sqrt }\\ \mbox\\ \end ==Formal definition== The real numbers ω1, ω2, ... , ω''n'' are said to be ''rationally dependent'' if there exist integers ''k''1, ''k''2, ... , ''k''''n'', not all of which are zero, such that :$k\_1\; \backslash omega\_1\; +\; k\_2\; \backslash omega\_2\; +\; \backslash cdots\; +\; k\_n\; \backslash omega\_n\; =\; 0.$ If such integers do not exist, then the vectors are said to be ''rationally independent''. This condition can be reformulated as follows: ω1, ω2, ... , ω''n'' are rationally independent if the only ''n''-tuple of integers ''k''1, ''k''2, ... , ''k''''n'' such that :$k\_1\; \backslash omega\_1\; +\; k\_2\; \backslash omega\_2\; +\; \backslash cdots\; +\; k\_n\; \backslash omega\_n\; =\; 0$ is the trivial solution in which every ''k''''i'' is zero. The real numbers form a vector space over the rational numbers, and this is equivalent to the usual definition of linear independence in this vector space. 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「Rational dependence」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.