Manuals/calci/HANKEL

MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)

• $TypeOfMatrix$ is the type of the matrix.
• $DimensionsOfMatrix$ 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.
• 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.MATRIX("hankel") = 0.312783548142761
• 2.MATRIX("hankel",3)

0.6414852568414062	0.9679132911842316	0.6076015164144337
0.9679132911842316	0.6076015164144337	0.6414852568414062
0.6076015164144337	0.6414852568414062	0.9679132911842316

• 3.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

• 4.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

• 5.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

References

• Hankel matrix

• List of Main Z Functions

• Z3 home