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Scilab Help >> Linear Algebra > Matrix Pencil > companion

# 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))```

• spec — eigenvalues, and eigenvectors of a matrix or a pencil
• poly — Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
• randpencil — random pencil