companion companion matrix

## Syntax

    A=companion(p)

## Arguments

p

  polynomial or vector of polynomials

A

  square matrix

## Description

Returns a matrix `A` with characteristic polynomial equal to `p` if `p` is monic. If `p` is not monic the characteristic polynomial of `A` is equal to `p/c` where `c` is the coefficient of largest degree in `p`.

If `p` is a vector of monic polynomials, `A` is block diagonal, and the characteristic polynomial of the ith block is `p(i)`.

## Examples

    s=poly(0,'s');
    p=poly([1,2,3,4,1],'s','c')
    det(s*eye(4,4)-companion(p))
    roots(p)
    spec(companion(p))

## See also

- spec
- poly
- randpencil