# compan

Companion matrix

## Syntax

```A = compan(u) ```

## Description

`A = compan(u)` returns the corresponding companion matrix whose first row is `-u(2:n)/u(1)`, where `u` is a vector of polynomial coefficients. The eigenvalues of `compan(u)` are the roots of the polynomial.

## Examples

collapse all

Compute the companion matrix corresponding to the polynomial $\left(x-1\right)\left(x-2\right)\left(x+3\right)={x}^{3}-7x+6$.

```u = [1 0 -7 6]; A = compan(u)```
```A = 3×3 0 7 -6 1 0 0 0 1 0 ```

The eigenvalues of `A` are the polynomial roots.

`eig(A)`
```ans = 3×1 -3.0000 2.0000 1.0000 ```

## Version History

Introduced before R2006a