Manuals/calci/hankel

HANKEL(Number)

• $Number$ is the order of the hankel matrix.

Description

• This function gives the matrix with the property of hankel matrix with the given order.
• A hankel matrix is a square matrix with constant skew diagonals.
• If the i,j element of Hankel matrix A is denoted $A_{i,j}$, then we have

$A_{i,j}=A_{i-1,j+1}$.

• i.e., The form of Hankel matrix is:

${\begin{bmatrix}a&b&c&d&e\\b&c&d&e&f\\c&d&e&f&g\\d&e&f&g&h\\e&f&g&h&i\\\end{bmatrix}}$.

• A hankel matrix is also called as catalecticant matrix.
• Here HANKEL(3) is gives the hankel matrix of order 3 with decimal values.
• A Hankel matrix is an upside-down Toeplitz matrix.
• A matrix whose entries along a parallel to the main anti-diagonal are equal, for each parallel.
• Sometimes this type of matrices are also called as orthosymmetric matrices.

Examples

1. hankel(2)

0.8035830636448866	0.8035830636448866
0.8035830636448866	0.001881340454530589

2. HANKEL(4)

0.3661268740416319	0.041098489444291175	0.5811984241396517	0.5811984241396517
0.041098489444291175	0.5811984241396517	0.5811984241396517	0.041098489444291175
0.5811984241396517	0.5811984241396517	0.041098489444291175	0.3661268740416319
0.5811984241396517	0.041098489444291175	0.3661268740416319	0.06363525915203883

See Also

• HANKEL
• HADAMARD
• hankel

References

• Hankel matrix

• List of Main Z Functions
• Z3 home