Hankel matrix
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In linear algebra, a Hankel matrix, named after Hermann Hankel, is a square matrix with constant (positive sloping) skew-diagonals, e.g.;
- <math>\begin{bmatrix}
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{bmatrix}<math>
In mathematical terms:
- <math>a_{i,j} = a_{i-1,j+1}<math>
The Hankel matrix is closely related to the Toeplitz matrix (a Hankel matrix is an upside-down Toeplitz matrix).
A Hankel operator on a Hilbert space is one whose matrix with respect to an orthonormal basis is an infinite Hankel matrix <math>(a_{i,j})_{i,j \ge 0}<math>, where <math> a_{i,j}<math> depends only on <math>i+j<math>.