Manuals/calci/HANKEL

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


  • is the type of the matrix.
  • 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

.

  • i.e., The form of Hankel matrix is:

.

  • 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
  • 6. MATRIX("hankel:integer")

-8

  • 7.MATRIX("hankel:positive integer")

61

  • 8.MATRIX("hankel:negative integer")

-73

Related Videos

Types of Matrices

See Also

References