翻訳と辞書 Words near each other ・ Identity Formation, Agency, and Culture ・ Identity fraud ・ Identity function ・ Identity FX ・ Identity Governance Framework ・ Identity Guard ・ Identity in social insects ・ Identity intelligence ・ Identity Interrogation ・ Identity Ireland ・ Identity line ・ Identity management ・ Identity management system ・ Identity management theory ・ Identity map pattern ・ Identity matrix ・ Identity negotiation ・ Identity of indiscernibles ・ Identity of Junius ・ Identity of the first male Muslim ・ Identity on Fire ・ Identity Performance ・ Identity Pieces ・ Identity politics ・ Identity preservation ・ Identity problem ・ Identity provider ・ Identity Registration Protocol ・ Identity score ・ Identity theft Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Identity matrix ： ウィキペディア英語版 Identity matrix In linear algebra, the identity matrix or unit matrix of size ''n'' is the ''n'' × ''n'' square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by ''I''''n'', or simply by ''I'' if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to ''I''.) Less frequently, some mathematics books use ''U'' or ''E'' to represent the identity matrix, meaning "unit matrix"〔.〕 and the German word "Einheitsmatrix",〔("Identity Matrix" ) on MathWorld;〕 respectively. :$$ I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \cdots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end When ''A'' is ''m''×''n'', it is a property of matrix multiplication that :$I\_mA\; =\; AI\_n\; =\; A.\; \backslash ,$ In particular, the identity matrix serves as the unit of the ring of all ''n''×''n'' matrices, and as the identity element of the general linear group GL(''n'') consisting of all invertible ''n''×''n'' matrices. (The identity matrix itself is invertible, being its own inverse.) Where ''n''×''n'' matrices are used to represent linear transformations from an ''n''-dimensional vector space to itself, ''In'' represents the identity function, regardless of the basis. The ''i''th column of an identity matrix is the unit vector ''ei''. It follows that the determinant of the identity matrix is 1 and the trace is ''n''. Using the notation that is sometimes used to concisely describe diagonal matrices, we can write: :$I\_n\; =\; \backslash mathrm(1,1,...,1).\; \backslash ,$ It can also be written using the Kronecker delta notation: :$(I\_n)\_\; =\; \backslash delta\_.\; \backslash ,$ The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another. The identity matrix of a given size is the only idempotent matrix of that size having full rank. That is, it is the only matrix such that (a) when multiplied by itself the result is itself, and (b) all of its rows, and all of its columns, are linearly independent. The principal square root of an identity matrix is itself, and this is its only positive definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.〔Mitchell, Douglas W. "Using Pythagorean triples to generate square roots of ''I''2". The Mathematical Gazette 87, November 2003, 499-500.〕 ==See also== *Binary matrix *Zero matrix *Unitary matrix *Matrix of ones 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「Identity matrix」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.