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 $A_{i,j}$, 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 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

1. MATRIX("hankel",5,1..10)

1	2	3	4	5
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8
5	6	7	8	9

1. MATRIX("hankel",5,-10..0)

-10	-9	-8	-7	-6
-9	-8	-7	-6	-5
-8	-7	-6	-5	-4
-7	-6	-5	-4	-3
-6	-5	-4	-3	-2

1. MATRIX("hankel",4,["rice","water"])

rice	water	rice	water
water	rice	water	rice
rice	water	rice	water
water	rice	water	rice

See Also

• ANTIDIAGONAL
• CONFERENCE
• CIRCULANT
• HADAMARD