翻訳と辞書 Words near each other ・ Jacobi ・ Jacobi (crater) ・ Jacobi (surname) ・ Jacobi coordinates ・ Jacobi eigenvalue algorithm ・ Jacobi elliptic functions ・ Jacobi field ・ Jacobi form ・ Jacobi group ・ Jacobi identity ・ Jacobi integral ・ Jacobi matrix ・ Jacobi Medical Center ・ Jacobi method ・ Jacobi method for complex Hermitian matrices ・ Jacobi operator ・ Jacobi polynomials ・ Jacobi Robinson ・ Jacobi rotation ・ Jacobi set ・ Jacobi sum ・ Jacobi symbol ・ Jacobi theta functions (notational variations) ・ Jacobi triple product ・ Jacobi zeta function ・ Jacobi's formula ・ Jacobi's four-square theorem ・ Jacobi's theorem ・ Jacobian ・ Jacobian conjecture 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 Jacobi operator ： ウィキペディア英語版 Jacobi operator A Jacobi operator, also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by a tridiagonal matrix in the standard basis given by Kronecker deltas. This operator is named after Carl Gustav Jacob Jacobi. == Self-adjoint Jacobi operators == The most important case is the one of self-adjoint Jacobi operators acting on the Hilbert space of square summable sequences over the positive integers $\backslash ell^2(\backslash mathbb)$. In this case it is given by :$J\backslash ,\; f(1)\; =\; a(1)\; f(2)\; +\; b(1)\; f(1),\; \backslash quad\; J\backslash ,\; f(n)\; =\; a(n)\; f(n+1)\; +\; a(n-1)\; f(n-1)\; +\; b(n)\; f(n),\; \backslash quad\; n>1,$ where the coefficients are assumed to satisfy :$a(n)\; >0,\; \backslash quad\; b(n)\; \backslash in\; \backslash mathbb.$ The operator will be bounded if and only if the coefficients are. There are close connections with the theory of orthogonal polynomials. In fact, the solution ''p''(''z'',''n'') of the recurrence relation :$J\backslash ,\; p(z,n)\; =\; z\backslash ,\; p(z,n),\; \backslash qquad\; p(z,1)=1\; \backslash text\; p\; (z,0)=0,$ is a polynomial of degree ''n'' − 1 and these polynomials are orthonormal with respect to the spectral measure corresponding to the first basis vector $\backslash delta\_1(n)=\; \backslash delta\_$. 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「Jacobi operator」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.