# Create Special Matrix (G Dataflow)

Generates a matrix of a specific type.

## matrix type

Type of matrix this node generates.

Let n represent the matrix size, x represent the input vector 1, nx represent the size of x, and y represent the input vector 2, ny represent the size of y, and B represent the output special matrix.

Name Value Description
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:

${b}_{0,j-1}=-\frac{{x}_{j}}{{x}_{o}}$, where 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. The 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.

Default: Identity

## vector 1

Matrix used to compose part of a Diagonal, Toeplitz, Vandermonde, Companion, or Hankel matrix.

This input accepts an array of double-precision, floating point numbers or array of complex double-precision, floating point numbers.

## vector 2

Matrix used to compose part of either a Toeplitz or Hankel matrix.

This input accepts an array of double-precision, floating point numbers or array of complex double-precision, floating point numbers.

## matrix size

Number of dimensions of the generated matrix.

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## special matrix

The generated matrix.

This output can return a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application