Hankel matrix
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Revision 1065
8/8/2026, 7:40:38 AM · Ancient Tree
Updated linked exercises
linked exercisesNoneDetermining a Hankel matrix
Revision 1064
8/8/2026, 7:40:25 AM · Ancient Tree
Updated text
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##### Intuition2
A Hankel matrix is a [[Matrix|matrix]] whose entries are constant along each [[anti-diagonal|anti-diagonal]]. For example:3
$$4
H=\left(\begin{array}{llll}5
1& 2& 3 & 4 \\6
2 & 3 & 4 & 5 \\7
3 & 4 & 5 & 6 \\8
4 & 5 & 6 & 79
\end{array}\right).10
$$11
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##### Definition13
A Hankel matrix is a matrix $H=(h_{ij})$ whose entries satisfy:14
$$h_{ij}=c_{i+j}$$15
for some [[Sequence|sequence]] $c_{k}$.16
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##### Remarks19
- Hankel matrices are not necessarily [[Square matrix|square]].Revision 1061
8/8/2026, 7:32:09 AM · Ancient Tree
Concept created
##### Intuition
A Hankel matrix is a [[Matrix|matrix]] whose entries are constant along each [[anti-diagonal|anti-diagonal]]. For example:
$$
H=\left(\begin{array}{llll}
1& 2& 3 & 4 \\
2 & 3 & 4 & 5 \\
3 & 4 & 5 & 6 \\
4 & 5 & 6 & 7
\end{array}\right).
$$
##### Definition
A Hankel matrix is a matrix $H=(h_{ij})$ whose entries satisfy:
$$h_{ij}=c_{i+j}$$
for some [[Sequence|sequence]] $c_{k}$.