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Generates one of the following types of matrix: Identity, Diagonal, Toeplitz, Vandermonde, Companion, Hankel, Hadamard, Wilkinson, Hilbert, Inverse Hilbert, Rosser, or Pascal.

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matrix type

Value specifying which type of matrix this node generates. Let n represent matrix size, X represent Input Vector1, nx represent the size of X, and Y represent Input Vector2, ny represent the size of Y, and B represent the output Special Matrix.

Identity 0

Generates an n-by-n identity matrix.

Diagonal 1 Generates an nx-by-nx diagonal matrix whose diagonal elements are the elements of X.
Toeplitz 2 Generates an nx-by-ny Toeplitz matrix, which has X as its first column and Y as its first row. If the first element of X and Y are different, the first element of X is used.
Vandermonde 3

Generates an nx-by-nx Vandermonde matrix whose columns are powers of the elements of X. The elements of a Vandermonde matrix are:

b i , j = x i n x j 1

where i , j = 0... n x 1 .

Companion 4 Generates an nx-1-by-nx-1 companion matrix. If vector X is a vector of a polynomial coefficient, the first element of X is the coefficient of the highest order, the last element of X is the constant term in the polynomial, the corresponding companion matrix is constructed as follows:
  • The first row is:

    b 0 , j 1 = x j x o , j = 1 , 2 , ... , n x 1
  • The rest of B from the second row is an identity matrix.
  • The eigenvalues of a companion matrix contain the roots of the corresponding polynomial.
Hankel 5 Generates an nx-by-ny Hankel matrix, where X is the first column and Y is the last row of the matrix. If the first element of Y and last element of X are different, this node uses the last element of X.
Hadamard 6 Generates an n-by-n Hadamard matrix, whose elements are 1 and -1. All columns or rows are orthogonal to each other. matrix size must be a power of 2, a power of 2 multiplied by 12, or a power of 2 multiplied by 20. If n is 1, this node returns an empty matrix.
Wilkinson 7 Generates an n-by-n Wilkinson matrix whose eigenvalues are ill-conditioned.
Hilbert 8

Generates an n-by-n Hilbert matrix, which has elements according to the following equation:

b i j = 1 i + j + 1

where i , j = 0 , 1 , ... n 1

Inverse Hilbert 9 Generates the inverse of an n-by-n Hilbert matrix.
Rosser 10 Generates an 8-by-8 Rosser matrix whose eigenvalues are ill-conditioned.
Pascal 11

Generates an n-by-n symmetric Pascal matrix, which has elements according to the following equation:

b i j = [ i + j i ]

where i , j = 0 , 1 , ... n 1

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matrix size

The number of dimensions of the output Special Matrix.

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input vector1

Matrix used to compose part of a Diagonal (1), Toeplitz (2), Vandermonde (3), Companion (4), or Hankel (5) matrix.

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input vector2

Matrix used to compose part of either a Toeplitz (2) or Hankel (5) matrix.

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special matrix

The generated matrix.

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error

A value that represents any error or warning that occurs when this node executes.