翻訳と辞書 Words near each other ・ Ski jumping at the 1988 Winter Olympics ・ Ski jumping at the 1988 Winter Olympics – Large hill individual ・ Ski jumping at the 1988 Winter Olympics – Large hill team ・ Ski jumping at the 1988 Winter Olympics – Normal hill individual ・ Ski jumping at the 1990 Asian Winter Games ・ Skew heap ・ Skew It on the Bar-B ・ Skew lattice ・ Skew lines ・ Skew normal distribution ・ Skew partition ・ Skew Peak ・ Skew polygon ・ Skew Siskin ・ Skew Siskin (album) ・ Skew-Hamiltonian matrix ・ Skew-Hermitian ・ Skew-Hermitian matrix ・ Skew-symmetric graph ・ Skew-symmetric matrix ・ Skew-T log-P diagram ・ Skewarkey Primitive Baptist Church ・ Skewb ・ Skewb Diamond ・ Skewb Ultimate ・ Skewbald ・ Skewbald Horde ・ Skewbald/Grand Union (EP) ・ Skewball ・ Skewed generalized t distribution 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 Skew-Hamiltonian matrix ： ウィキペディア英語版 Skew-Hamiltonian matrix In linear algebra, skew-Hamiltonian matrices are special matrices which correspond to skew-symmetric bilinear forms on a symplectic vector space. Let ''V'' be a vector space, equipped with a symplectic form $\backslash Omega$. Such a space must be even-dimensional. A linear map $A:\backslash ;\; V\; \backslash mapsto\; V$ is called a skew-Hamiltonian operator with respect to $\backslash Omega$ if the form $x,\; y\; \backslash mapsto\; \backslash Omega(A(x),\; y)$ is skew-symmetric. Choose a basis $e\_1,\; ...\; e\_$ in ''V'', such that $\backslash Omega$ is written as $\backslash sum\_i\; e\_i\; \backslash wedge\; e\_$. Then a linear operator is skew-Hamiltonian with respect to $\backslash Omega$ if and only if its matrix ''A'' satisfies $A^T\; J\; =\; J\; A$, where ''J'' is the skew-symmetric matrix :$J=$ \begin 0 & I_n \\ -I_n & 0 \\ \end and ''In'' is the $n\backslash times\; n$ identity matrix.〔William C. Waterhouse, (''The structure of alternating-Hamiltonian matrices'' ), Linear Algebra and its Applications, Volume 396, 1 February 2005, Pages 385-390〕 Such matrices are called skew-Hamiltonian. The square of a Hamiltonian matrix is skew-Hamiltonian. The converse is also true: every skew-Hamiltonian matrix can be obtained as the square of a Hamiltonian matrix.〔〔 Heike Faßbender, D. Steven Mackey, Niloufer Mackey and Hongguo Xu (Hamiltonian Square Roots of Skew-Hamiltonian Matrices, ) Linear Algebra and its Applications 287, pp. 125 - 159, 1999〕 ==Notes== 〔 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「Skew-Hamiltonian 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.