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Math Help - Vector space polynomials

  1. #1
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    Post Vector space polynomials

    Hi,
    I am trying to complete a question in preparation for my exams next month, but I am struggling to get my head around the whole concept of it.
    Here it is...

    Let N be a positive integer, and let Vn of R(X) be the vector space of polynomials with real coefficients and degree at most N. Consider the derivative D on Vn:
    D : Vn Vn
    f(x) f '(x) and the composite map D^(2)= D D : Vn Vn

    (i) Show that D and D^(2) are linear
    (ii) Compute the rank and nullity of the map D^(2)
    (iii) Decide whether D is diagonizable

    I would really appreciate any help for any part of this question!
    Thanks in advance,
    Katie
    Last edited by katiedavies1990; December 6th 2009 at 10:08 AM.
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