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.
• 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.