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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 Nullity theorem ： ウィキペディア英語版 Nullity theorem The nullity theorem is a mathematical theorem about the inverse of a partitioned matrix, which states that the nullity of a block in a matrix equals the nullity of the complementary block in its inverse matrix. Here, the nullity is the dimension of the kernel. The theorem was proven in an abstract setting by , and for matrices by . Partition a matrix and its inverse in four submatrices: : The partition on the right-hand side should be the transpose of the partition on the left-hand side, in the sense that if ''A'' is an ''m''-by-''n'' block then ''E'' should be an ''n''-by-''m'' block. The statement of the nullity theorem is now that the nullities of the blocks on the right equal the nullities of the blocks on the left : :$\backslash begin$ \operatorname \, A &= \operatorname \, H, \\ \operatorname \, B &= \operatorname \, F, \\ \operatorname \, C &= \operatorname \, G, \\ \operatorname \, D &= \operatorname \, E. \end More generally, if a submatrix is formed from the rows with indices and the columns with indices , then the complementary submatrix is formed from the rows with indices \ and the columns with indices \ , where ''N'' is the size of the whole matrix. The nullity theorem states that the nullity of any submatrix equals the nullity of the complementary submatrix of the inverse. == References == * . * . * . 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「Nullity 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.