Manuals/calci/hankel

HANKEL(Number)

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

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

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

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.

1. hankel(2)

0.8035830636448866	0.8035830636448866
0.8035830636448866	0.001881340454530589

2. HANKEL(4)