1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

ODE, Establish criteria for f in Range(L)

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Let Z={x: {0,1,..,5} → ℝ^n} (column vector with real entries) and define T:Z→ℝ^n by Tz = z(0) - z(5). Let X = Ker(T) and let Y={y: {0,1,..,4}→ℝ^n}. Define L:X→Y by
    (Lx)(t) = x(t+1) - Ax(t) where A is an invertible matrix.

    Establish criteria for f in Range(L).

    2. Relevant equations

    3. The attempt at a solution

    I know for f to be in Range(L) there exists x in X such that L(x) = f
    so (Lx)(t) = f(t) for all t,
    then x(t+1) - Ax(t) = f(t) for all t,
    or x(t+1) = Ax(t) + f(t).
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: ODE, Establish criteria for f in Range(L)
  1. Finding range of f(x) (Replies: 13)