# How to convert polynomial to matrix?

1. Apr 18, 2004

### m2006

How to convert polynomial to matrix???

Does anyone know how to convert a polynomial to a matrix. I have been told that it is possible to convert a fourth order polynomial to a 4x4 Matrix in Matlab but I have no clue how to go about it and how it is done. Any suggestions or even where to look would be GREATLY helpful!

2. Apr 19, 2004

### billk

Can you be more specific about what you are trying to do?

If you were to choose a basis for the space of fourth degree polynomials, like $$\{ 1,x,x^2,x^3,x^4 \}$$, then it is possible to represent a polynomial as an element of this vector space by a coefficient matrix.

For example, $$3x^4-2x^2+5 \mapsto \left[5,0,-2,0,3 \right]$$. This is not a 4x4 matrix like you are looking for, but it is a representation of the polynomial as a matrix.

If you are more specific about what you are trying to do, maybe I can offer more insight, although I am not sure if what you want can be done.

3. Apr 11, 2011

### thamster

Re: How to convert polynomial to matrix???

check this out for making a companion matrix for a given polynomial:
http://en.wikipedia.org/wiki/Companion_matrix

The determinant of a companion matrix is a polynomial in λ, known as the characteristic polynomial. λs are the eigenvalues, they are also the solutions to the polynomial.

This works well for polynomials of degree 4 or smaller since they can be solved by a finite sequence of arithmetic operations and radicals.

hope this helps.

4. Apr 22, 2011

### spg89

Re: How to convert polynomial to matrix???

use cayley-Hamilton theorem from backwards,it will help...