companion

Scilab Function
Last update : 25/04/2007

companion - companion matrix

### Calling Sequence

  `A=companion(p)`

### Parameters

- `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()-companion(p))
    roots(p)
    spec(companion(p))

### See Also

`spec` , `poly` , `randpencil` ,

### Author

F.D.