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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 Hankel matrix ： ウィキペディア英語版 Hankel matrix In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.: :$\backslash begin$ a & b & c & d & e \\ b & c & d & e & f \\ c & d & e & f & g \\ d & e & f & g & h \\ e & f & g & h & i \\ \end. Any ''n''×''n'' matrix ''A'' of the form $$ A = \begin a_ & a_ & a_ & \ldots & \ldots &a_ \\ a_ & a_2 & & & &\vdots \\ a_ & & & & & \vdots \\ \vdots & & & & & a_\\ \vdots & & & & a_& a_ \\ a_ & \ldots & \ldots & a_ & a_ & a_ \end is a Hankel matrix. If the ''i'',''j'' element of ''A'' is denoted ''A''''i'',''j'', then we have :$A\_\; =\; A\_\; =\; a\_.\backslash$ The Hankel matrix is closely related to the Toeplitz matrix (a Hankel matrix is an upside-down Toeplitz matrix). For a special case of this matrix see Hilbert matrix. A Hankel operator on a Hilbert space is one whose matrix with respect to an orthonormal basis is a (possibly infinite) Hankel matrix $(A\_)\_$, where $A\_$ depends only on $i+j$. The determinant of a Hankel matrix is called a catalecticant. ==Hankel transform== The Hankel transform is the name sometimes given to the transformation of a sequence, where the transformed sequence corresponds to the determinant of the Hankel matrix. That is, the sequence $\backslash \_$ is the Hankel transform of the sequence $\backslash \_$ when :$h\_n\; =\; \backslash det\; (b\_)\_.$ Here, $a\_=b\_$ is the Hankel matrix of the sequence $\backslash$. The Hankel transform is invariant under the binomial transform of a sequence. That is, if one writes :$c\_n\; =\; \backslash sum\_^n\; b\_k$ as the binomial transform of the sequence $\backslash$, then one has :$\backslash det\; (b\_)\_\; =\; \backslash det\; (c\_)\_.$ 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「Hankel 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.