1. Not finding help here? Sign up for a free 30min 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!

EigenValues and EigenVectors.

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the eigenvalues and eigenvectors of P = {(0.8 0.6), (0.2 0.4)}. Express {(1), (0)} and {(0), (1)} as sums of eigenvectors.



    2. Relevant equations
    Row ops and det(P - λI) = 0.


    3. The attempt at a solution
    I've found the eigenvectors and eigenvalues of P to be 1 with t{(3), (1)} and 0.2 with q{(-1), (1)} were t and q are arbitrary (parameters). How do I express the two other vectors (in the question statement) as sums of eigenvectors? Thanks.
     
  2. jcsd
  3. Apr 24, 2013 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Unless there's another condition you need to satisfy, you can take t=q=1, so the problem is asking you now to solve
    $$\begin{pmatrix} 1 \\ 0 \end{pmatrix} = a\begin{pmatrix} 3 \\ 1 \end{pmatrix}+b\begin{pmatrix} -1 \\ 1 \end{pmatrix}$$ which is just a system of two equations and two unknowns. And then do the same thing for the other vector.
     
  4. Apr 24, 2013 #3
    Cool. Got it now. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: EigenValues and EigenVectors.
Loading...