翻訳と辞書 Words near each other ・ Unitarity (physics) ・ Unitarity gauge ・ Unitary ・ Unitary authorities of England ・ Unitary authority ・ Unitary controller ・ Unitary Democratic Coalition ・ Unitary development plan ・ Unitary divisor ・ Unitary enterprise ・ Unitary equivalence ・ Unitary executive theory ・ Unitary Federation of Petroleum and Gas Workers ・ Unitary Front ・ Unitary group ・ Unitary matrix ・ Unitary method ・ Unitary National Liberation Front ・ Unitary operator ・ Unitary parliamentary republic ・ Unitary patent ・ Unitary patent (Switzerland and Liechtenstein) ・ Unitary perfect number ・ Unitary Plan Wind Tunnel (Mountain View, California) ・ Unitary psychosis ・ Unitary representation ・ Unitary Socialist Party ・ Unitary state ・ Unitary theories of memory ・ Unitary transformation 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 Unitary matrix ： ウィキペディア英語版 Unitary matrix In mathematics, a complex square matrix ''U'' is unitary if its conjugate transpose ''U''∗ is also its inverse – that is, if ::$U^$ * U = UU^ * = I , where ''I'' is the identity matrix. In physics, especially in quantum mechanics, the Hermitian conjugate of a matrix is denoted by a dagger (†) and the equation above becomes ::$U^\backslash dagger\; U\; =\; UU^\backslash dagger\; =\; I\; .$ The real analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes. ==Properties== For any unitary matrix ''U'' of finite size, the following hold: *Given two complex vectors ''x'' and ''y'', multiplication by ''U'' preserves their inner product; that is, :$\backslash langle\; Ux,\; Uy\; \backslash rangle\; =\; \backslash langle\; x,\; y\; \backslash rangle$. *''U'' is normal *''U'' is diagonalizable; that is, ''U'' is unitarily similar to a diagonal matrix, as a consequence of the spectral theorem. Thus ''U'' has a decomposition of the form ::$U\; =\; VDV^$ *\; :where ''V'' is unitary and ''D'' is diagonal and unitary. * $\backslash left|\; \backslash det\; (\; U\; )\; \backslash right|\; =\; 1$. * Its eigenspaces are orthogonal. * ''U'' can be written as , where ''e'' indicates matrix exponential, is the imaginary unit and ''H'' is an Hermitian matrix. For any nonnegative integer ''n'', the set of all ''n''-by-''n'' unitary matrices with matrix multiplication forms a group, called the unitary group U(''n''). Any square matrix with unit Euclidean norm is the average of two unitary matrices. 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「Unitary 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.