Editing Hankel matrix (section)

{{Short description|Square matrix in which each ascending skew-diagonal from left to right is constant}}
In [[linear algebra]], a '''Hankel matrix''' (or '''[[catalecticant]] matrix'''), named after [[Hermann Hankel]], is a rectangular matrix in which each ascending skew-diagonal from left to right is constant. For example,

<math display=block>\qquad\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>

More generally, a '''Hankel matrix''' is any <math>n \times n</math> [[matrix (mathematics)|matrix]] <math>A</math> of the form

<math display=block>A = \begin{bmatrix}
  a_0 & a_1 & a_2 & \ldots & a_{n-1}  \\
  a_1 & a_2 &  &  &\vdots \\
  a_2 &  &  & & a_{2n-4} \\ 
 \vdots & &  & a_{2n-4} & a_{2n-3} \\
a_{n-1} &  \ldots & a_{2n-4} & a_{2n-3} & a_{2n-2}
\end{bmatrix}.</math>

In terms of the components, if the <math>i,j</math> element of <math>A</math> is denoted with <math>A_{ij}</math>, and assuming <math>i \le j</math>, then we have <math>A_{i,j} = A_{i+k,j-k}</math> for all <math>k = 0,...,j-i.</math>