MATRIX("HANKEL",order)
- 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 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
, 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.
- 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
References