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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 Central polynomial ： ウィキペディア英語版 Central polynomial In algebra, a central polynomial for ''n''-by-''n'' matrices is a polynomial in non-commuting variables that is non-constant but yields a scalar matrix whenever it is evaluated at ''n''-by-''n'' matrices. That such polynomials exist for any square matrices was discovered in 1970 independently by Formanek and Razmyslov. The term "central" is because the evaluation of a central polynomial has the image lying in the center of the matrix ring over any commutative ring. The notion has an application to the theory of polynomial identity rings. Example: $(xy\; -\; yx)^2$ is a central polynomial for 2-by-2-matrices. Indeed, by the Cayley–Hamilton theorem, one has that $(xy\; -\; yx)^2\; =\; -\backslash det(xy\; -\; yx)I$ for any 2-by-2-matrices ''x'', ''y''. == See also == *Generic matrix ring 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「Central polynomial」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.