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

## 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: ${b}_{i,j}={x}_{i}^{nx-j-1}$ where $i,j=0...nx-1$. 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: ${b}_{0,j-1}=-\frac{{x}_{j}}{{x}_{o}},j=1,2,...,nx-1$ 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: ${b}_{ij}=\frac{1}{i+j+1}$ 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: ${b}_{ij}=\left[\begin{array}{c}i+j\\ i\end{array}\right]$ where $i,j=0,1,...n-1$

## matrix size

The number of dimensions of the output Special Matrix.

## input vector1

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

## input vector2

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

## special matrix

The generated matrix.

## error

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