# Create Real Matrix from Eigenvalues (G Dataflow)

Generates a real matrix from a specified set of eigenvalues.

## eigenvalues

Eigenvalues from which to create the real matrix. Eigenvalues must be real or conjugate pairs.

## 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

## matrix

Real matrix whose eigenvalues you specified.

## 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.

## Algorithm for Calculating the Eigenvalues

This node generates the output matrix in the following form:

${\left[\begin{array}{cccccc}0& 1& 0& \cdots & \cdots & 0\\ 0& 0& 1& 0& \cdots & 0\\ ⋮& \ddots & \ddots & \ddots & \ddots & ⋮\\ 0& \cdots & \cdots & 0& 1& 0\\ 0& \cdots & \cdots & \cdots & 0& 1\\ -{a}_{0}& -{a}_{1}& -{a}_{2}& \cdots & -{a}_{n-2}& -{a}_{n-1}\end{array}\right]}_{n×n}$

where n is the length of the input eigenvalues and a 0, a 1, ..., a n-1 are the coefficients of the polynomial P(x).

The following equation defines P(x):

$P\left(x\right)=\left(x-{\lambda }_{0}\right)\left(x-{\lambda }_{1}\right)\dots \left(x-{\lambda }_{n-1}\right)={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\dots +{a}_{n-1}{x}^{n-1}+{x}^{n}$

where λ0, λ1, ..., λ n - 1 are the elements in eigenvalues.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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