# 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.

Default: No error

## matrix

Real matrix whose eigenvalues you specified.

## error out

Error information. The node produces this output according to standard error behavior.

## 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 a0, a1, ..., an-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, ..., λn - 1 are the elements in eigenvalues.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported