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Converting equations into vectores

  1. Dec 30, 2011 #1
    1. The problem statement, all variables and given/known data

    How do I convert a polinomial equation into a vector? Example:

    x^2 + 3x + 1 How do I convert it into a vector like (x,y,z) (with as many variables as possible

    2. Relevant equations



    3. The attempt at a solution

    The only thing I could remember was to isolate each x into a different vector, but I'm pretty sure I learned to do it in a better way at class, just don't remember it

    x^2(1,0,0) + x(0,3,0 + (0,0,1)

    Thanks ahead
     
    Last edited by a moderator: Dec 30, 2011
  2. jcsd
  3. Dec 30, 2011 #2

    Mark44

    Staff: Mentor

    I'm guessing that you are working with function spaces, which are similar to vector spaces. In a vector space, the coordinates of a given vector indicate a particular linear combination of basis vectors. For example, in R3, the standard basis is e1 = <1, 0, 0>, e2 = <0, 1, 0>, and e3 = <0, 0, 1>.

    The vector <3, -1, 2> = 3e1 + (-1)e2 + 2e3.

    In the function space of polynomials of degree 2 or less (P2), one basis is the set of functions {1, x, x2}. You can represent any polynomial of degree two or less as a linear combination of these basis functions.
     
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