gives the n×n Hankel matrix with first row and first column being successive integers.


gives the Hankel matrix whose first column consists of elements c1, c2, .

HankelMatrix[{c1,c2,,cm},{r1,r2,, rn}]

gives the Hankel matrix with elements ci down the first column, and ri across the last row.


  • The element cm must be the same as r1. »


open allclose all

Basic Examples  (3)

4×4 Hankel matrix:

Scope  (4)

Make a Hankel matrix of machine numbers:

Make a Hankel matrix with 24-digit precision:

Complex entries:

Non-square Hankel matrices:

Properties & Relations  (5)

Size-20 Hankel matrix:

The determinant of the Hankel matrix of size is :

A square Hankel matrix with real entries is symmetric:

HankelMatrix[c,RotateRight[c]] is a square anticirculant matrix:

Square anticirculant matrices have eigenvector {1,} with eigenvalue c1+c2+:

HankelMatrix and ToeplitzMatrix are related by a reversed identity matrix:

Possible Issues  (1)

If element cm is not the same as r1, cm is used and r1 is ignored:

Neat Examples  (1)

Introduced in 2007