Manuals/calci/HANKEL

HANKEL

MATRIX("HANKEL",order)

• $order$ 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{i,j}} , then we have

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{i,j} = A_{i-1,j+1}} .

• i.e., The form of Hankel matrix is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 MATRIX("hankel") 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.
• Equivalently, is a Hankel matrix if and only if there exists a sequence, such that ,If are square matrices, then is referred to as a block Hankel matrix.

Examples

1. MATRIX("hankel")

0.6414852568414062	0.9679132911842316	0.6076015164144337
0.9679132911842316	0.6076015164144337	0.6414852568414062
0.6076015164144337	0.6414852568414062	0.9679132911842316