Manuals/calci/HANKEL

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)
 0.641485 0.967913 0.607602 0.967913 0.607602 0.641485 0.607602 0.641485 0.967913
• 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

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