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!

Repeated Eigenvalues

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve X' = [ [9, 4, 0], [-6, -1, 0], [6, 4, 3]] * X using eigenvalues.

    2. Relevant equations
    (A - λI) * K = 0
    X = eλt

    3. The attempt at a solution
    Set up the characteristic equation to find eigenvalues. I found a root of multiplicity 2 of λ=3 and another distinct root λ=5.

    When setting up equations to solve for the eigenvectors (setting λ= 3) I found:

    6k1 + 4k2 = 0
    -6k1 -4k2 = 0
    6k1 + 4k2 = 0

    So there's only a dependency for k1 and k2. So can't I simply find two linearly independent eigenvectors by substituting different values for k3 such as [2, -3, 1] and [2, -3, 2] and use those as two independent solutions? Or does this mean I still have to walk through the steps of using the Kteλt + Peλt form of the solution to find the second solution for the λ=3 root?
  2. jcsd
  3. Nov 24, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: Repeated Eigen Values

    Your first method is the right one.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook