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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 Splitting lemma (functions) ： ウィキペディア英語版 Splitting lemma (functions) : ''See also splitting lemma in homological algebra.'' In mathematics, especially in singularity theory the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point. ==Formal statement== Let $\backslash scriptstyle\; f:(\backslash mathbb^n,0)\backslash to(\backslash mathbb,0)$ be a smooth function germ, with a critical point at 0 (so $\backslash scriptstyle\; (\backslash partial\; f/\backslash partial\; x\_i)(0)=0,\backslash ;(i=1,\backslash dots,\; n)$). Let ''V'' be a subspace of $\backslash scriptstyle\backslash mathbb^n$ such that the restriction ''f|V'' is non-degenerate, and write ''B'' for the Hessian matrix of this restriction. Let ''W'' be any complementary subspace to ''V''. Then there is a change of coordinates $\backslash Phi(x,y)$ of the form $\backslash Phi(x,y)\; =\; (\backslash phi(x,y),y)$ with $\backslash scriptstyle\; x\backslash in\; V,\backslash ;y\backslash in\; W$, and a smooth function ''h'' on ''W'' such that :$f\backslash circ\backslash Phi(x,y)\; =\; \backslash textstyle\backslash frac12\; x^TBx\; +\; h(y).$ This result is often referred to as the parametrized Morse lemma, which can be seen by viewing ''y'' as the parameter. It is the ''gradient version'' of the implicit function theorem. 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「Splitting lemma (functions)」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.