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How to convert polynomial to matrix?

  1. Apr 18, 2004 #1
    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. :confused: Any suggestions or even where to look would be GREATLY helpful!
  2. jcsd
  3. Apr 19, 2004 #2
    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 [tex] \{ 1,x,x^2,x^3,x^4 \} [/tex], then it is possible to represent a polynomial as an element of this vector space by a coefficient matrix.

    For example, [tex] 3x^4-2x^2+5 \mapsto \left[5,0,-2,0,3 \right] [/tex]. 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.
  4. Apr 11, 2011 #3
    Re: How to convert polynomial to matrix???

    check this out for making a companion matrix for a given polynomial:

    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.
  5. Apr 22, 2011 #4
    Re: How to convert polynomial to matrix???

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