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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 Peirce decomposition ： ウィキペディア英語版 Peirce decomposition In algebra, a Peirce decomposition is a decomposition of an algebra as a sum of eigenspaces of commuting idempotent elements. The Peirce decomposition for associative algebras was introduced by . A similar but more complicated Peirce decomposition for Jordan algebras was introduced by . ==Peirce decomposition for associative algebras== If ''e'' is an idempotent (''e''2=''e'') in an associative algebra ''A'', then the two-sided Peirce decomposition writes ''A'' as the direct sum of ''eAe'', ''eA''(1−''e''), (1−''e'')''Ae'', and (1−''e'')''A''(1−''e''). There are also left and right Peirce decompositions, where the left decomposition writes ''A'' as the direct sum of ''eA'' and (1−''e'')''A'', and the right one writes ''A'' as the direct sum of ''Ae'' and ''A''(1−''e''). More generally, if ''e''1,...,''e''''n'' are commuting idempotents with sum 1, then ''A'' is the direct sum of the spaces ''e''''i''''Ae''''j'' for 1≤''i'',''j''≤''n''. 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「Peirce decomposition」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.