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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 Cartan's lemma ： ウィキペディア英語版 Cartan's lemma In mathematics, Cartan's lemma refers to a number of results named after either Élie Cartan or his son Henri Cartan: * In exterior algebra:〔 *〕 Suppose that ''v''1, ..., ''v''''p'' are linearly independent elements of a vector space ''V'' and ''w''1, ..., ''w''''p'' are such that ::$v\_1\backslash wedge\; w\_1\; +\; \backslash cdots\; +\; v\_p\backslash wedge\; w\_p\; =\; 0$ :in Λ''V''. Then there are scalars ''h''''ij'' = ''h''''ji'' such that ::$w\_i\; =\; \backslash sum\_^p\; h\_v\_j.$ * In several complex variables: Let and and define rectangles in the complex plane C by ::$\backslash begin$ K_1 &= \ \\ K_1' &= \ \\ K_1'' &= \ \end :so that $K\_1\; =\; K\_1\text{'}\backslash cap\; K\_1\text{'}\text{'}$. Let ''K''2, ..., ''K''''n'' be simply connected domains in C and let ::$\backslash begin$ K &= K_1\times K_2\times\cdots \times K_n\\ K' &= K_1'\times K_2\times\cdots \times K_n\\ K'' &= K_1''\times K_2\times\cdots \times K_n \end :so that again $K\; =\; K\text{'}\backslash cap\; K\text{'}\text{'}$. Suppose that ''F''(''z'') is a complex analytic matrix-valued function on a rectangle ''K'' in C''n'' such that ''F''(''z'') is an invertible matrix for each ''z'' in ''K''. Then there exist analytic functions $F\text{'}\backslash ,$ in $K\text{'}\backslash ,$ and $F\text{'}\text{'}\backslash ,$ in $K\text{'}\text{'}\backslash ,$ such that ::$F(z)\; =\; F\text{'}(z)F\text{'}\text{'}(z)\backslash ,$ :in ''K''. * In potential theory, a result that estimates the Hausdorff measure of the set on which a logarithmic Newtonian potential is small. See Cartan's lemma (potential theory). ==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「Cartan's lemma」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.