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Hankel matrix
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==Properties== * Any Hankel matrix is [[symmetric matrix|symmetric]]. * Let <math>J_n</math> be the <math>n \times n</math> [[exchange matrix]]. If <math>H</math> is an <math>m \times n</math> Hankel matrix, then <math>H = T J_n</math> where <math>T</math> is an <math>m \times n</math> [[Toeplitz matrix]]. ** If <math>T</math> is [[real number|real]] symmetric, then <math>H = T J_n</math> will have the same [[eigenvalue]]s as <math>T</math> up to sign.<ref name="simax1">{{cite journal | last = Yasuda | first = M. | title = A Spectral Characterization of Hermitian Centrosymmetric and Hermitian Skew-Centrosymmetric K-Matrices | journal = SIAM J. Matrix Anal. Appl. | volume = 25 | issue = 3 | pages = 601β605 | year = 2003 | doi = 10.1137/S0895479802418835}}</ref> * The [[Hilbert matrix]] is an example of a Hankel matrix. * The [[determinant]] of a Hankel matrix is called a [[catalecticant]].
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