How to convert polynomial to matrix???

by m2006
Tags: convert, matrix, polynomial
 P: 1 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!
 P: 3 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.
 P: 1 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.
P: 7

How to convert polynomial to matrix???

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

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