1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear transformation and polynomial function

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data
    from calculus we know that ,for any polynomial function f : R-R of degree <= n,the fuction of I(f) :R-R ,s----[tex]\int[/tex]f(u) du is a polynomial function of degree <=n+1
    show that the map I: Pn--Pn+1 , f--I(f) is an injective linear transformation, determine a basis of the image of I and find the matrix M[tex]\in[/tex]M(n+2)*(n+1)(R) that represents I with respect to the basis 1,t,......t^n of Pn and the basis 1,t,........t^(n+1) of Pn+1

    2. Relevant equations

    3. The attempt at a solution
    can i use L(x+y)=L(x)+L(y) aL(x)=L(ax) to show linear transformation ? but for what value i can choose for x, y
    for ''determine ......'' part i have no idea for it ,any help ?
  2. jcsd
  3. Apr 29, 2009 #2


    Staff: Mentor

    No, you can't use these -- you have to show that they hold for this transformation. For x and y, use polynomial functions of degree <= n. For example, you could let f(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a1x + a0, and g(x) = bnxn + bn-1xn-1 + bn-2xn-2 + ... + b1x + b0.
    Then show that L(f + g) = L(f) + L(g) and that aL(f) = L(ax).

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Linear transformation polynomial Date
Matrix of linear transformation Mar 27, 2016
Linear Transformation and isomorphisms Aug 30, 2015
Polynomial Linear Transformation Mar 22, 2013
Linear Polynomial Transformation Feb 4, 2013
Linear Algebra - Linear Transformation of a polynomial Dec 5, 2011