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!

Homework Help: Iterated maps and eigenvalues and vectors

  1. Jul 29, 2008 #1
    Totaly stuck on this one cant even start to fathom an attempt. first part of the question is show that the eigenvalues of the matrix (2x2 left to right) 4,-1,-4,4 are sigma1=2 and sigma2 =2 and eigenvectors e1= (1,2)T and e2=(1,-2)T done this no problem but am writing this as the second part of the question says

    use this result to find the solution to the 2 dimensional linear map

    Xn+1 =4Xn -Yn
    Yn+1 =-4Xn+4Yn

    with X0=1 and y0=1

    please help as i have no idea where to even begin. thanks
    Last edited: Jul 29, 2008
  2. jcsd
  3. Jul 29, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Call v_n the vector (x_n,y_n) and M your given matrix. Then the iteration is v_n+1=M*v_n. So v_n=M^n*v_0. You'll find this easy to express explicitly if you write v_0=(1,1) as a linear combination of eigenvectors of M.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook