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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 Chebotaryov theorem on roots of unity ： ウィキペディア英語版 Chebotaryov theorem on roots of unity The theorem state that all submatrices of a DFT matrix of prime length are invertible. The Chebotaryov theorem on roots of unity was originally a conjecture made by Ostrowski in the context of lacunary series. Chebotaryov was the first to prove it, in the 1930s. This proof involves tools from Galois theory and did not please Ostrowski, who made comments arguing that it "''does not meet the requirements of mathematical esthetics''" .〔Stevenhagen et Al., 1996〕 Several proofs have been proposed since,〔P.E. Frenkel,2003〕 and it has even been discovered independently by Dieudonné.〔J. Dieudonné, 1970〕 == Statement == Let $\backslash Omega$ be a matrix with entries $a\_\; =\backslash omega^,1\backslash leq\; i,j\backslash leq\; n$, where $\backslash omega\; =e^,n\backslash in\; \backslash mathbb$. If $n$ is prime then any minor of $\backslash Omega$ is non-zero. 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「Chebotaryov theorem on roots of unity」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.