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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 Latimer–MacDuffee theorem ： ウィキペディア英語版 Latimer–MacDuffee theorem The Latimer–MacDuffee theorem is a theorem in abstract algebra, a branch of mathematics. Let $f$ be a monic, irreducible polynomial of degree $n$. The Latimer–MacDuffee theorem gives a one-to-one correspondence between $\backslash mathbb$-similarity classes of $n\backslash times\; n$ matrices with characteristic polynomial $f$ and the ideal classes in the order :$\backslash mathbb()/(f(x)).\; \backslash ,$ where ideals are considered equivalent if they are equal up to an overall (nonzero) rational scalar multiple. (Note that this order need not be the full ring of integers, so nonzero ideals need not be invertible.) Since an order in a number field has only finitely many ideal classes (even if it is not the maximal order, and we mean here ideals classes for all nonzero ideals, not just the invertible ones), it follows that there are only finitely many conjugacy classes of matrices over the integers with characteristic polynomial $f(x)$. ==References== * Claiborne G. Latimer and C. C. MacDuffee, ("A Correspondence Between Classes of Ideals and Classes of Matrices" ), ''Annals of Mathematics'', 1933. 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「Latimer–MacDuffee theorem」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.