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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 Drazin inverse ： ウィキペディア英語版 Drazin inverse In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix. Let ''A'' be a square matrix. The index of ''A'' is the least nonnegative integer ''k'' such that rank(''A''''k''+1) = rank(''A''''k''). The Drazin inverse of ''A'' is the unique matrix ''A''''D'' which satisfies :$A^\; A^D=A^k,\; \backslash quad\; A^D\; A\; A^D=A^D,\backslash quad\; A\; A^D=\; A^D\; A.$ * If ''A'' is invertible with inverse $A^$, then $A^D=A^$. * The Drazin inverse of a matrix of index 0 or 1 is called the group inverse or -inverse and denoted ''A''#. The group inverse can be defined, equivalently, by the properties ''AA''#''A'' = ''A'', ''A''#''AA''# = ''A''#, and ''AA''# = ''A''#''A''. * A projection matrix ''P'', defined as a matrix such that ''P''2 = ''P'', has index 1 (or 0) and has Drazin inverse ''P''''D'' = ''P''. * If A is a nilpotent matrix (for example a shift matrix), then $A^D=0.$ The hyper-power sequence is :$A\_:=A\_i+A\_i\backslash left(I-\; A\; A\_i\backslash right);$ for convergence notice that $A\_=A\_i\; \backslash sum\_^\; (I-A\; A\_i)^k.$ For $A\_0:=\backslash alpha\; A$ or any regular $A\_0$ with $A\_0\; A=\; A\; A\_0$ chosen such that the sequence tends to its Drazin inverse, :$A\_i\; \backslash rightarrow\; A^D.$ == See also== * Constrained generalized inverse * Inverse element * Moore–Penrose inverse 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「Drazin inverse」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.