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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.: : Any ''n''×''n'' matrix ''A'' of the form is a Hankel matrix. If the ''i'',''j'' element of ''A'' is denoted ''A''''i'',''j'', then we have : 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 , where depends only on . 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 is the Hankel transform of the sequence when : Here, is the Hankel matrix of the sequence . The Hankel transform is invariant under the binomial transform of a sequence. That is, if one writes : as the binomial transform of the sequence , then one has : 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
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