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!

Confused with eigenvector

  1. May 31, 2012 #1
    Hello people!

    I am having a bit trouble with verifying my result when i compute the eigenvectors for the following matrix:

    A=[[3,4],[3,2]]

    I know for sure that the eigenvalues is respectively -1 and 6, so i start finding a solution for the following null spaces:

    1) N(A--1I)=[[4,4|0],[3,3|0]]~[[1,1|0],[0,0|0]] => x1 = x2 so the the vector x2[1,-1] will be a solution and therefor the first eigenvector is [1,-1]

    2) N(A-6I)=[[-3,4|0],[3,-4|0]]~[[1,-4/3|0],[0,0|0]] => x1=4/3 so this indicate that x2[-4/3,1] will be a solution to the null space, and therefor the second eigen vector i [-4/3,1].

    However the result should be [1,-1] [4,3] respectively. What am i doing wrong?
     
  2. jcsd
  3. May 31, 2012 #2
    [-4/3,1] is not an eigenvector of 6. The correct eigenvector is [4/3,1] because the equation you get is 3x-4y=0.
     
  4. May 31, 2012 #3

    phyzguy

    User Avatar
    Science Advisor

    Eigenvectors are always undermined up to a multiplicative factor, since if A*x = λ*x, then
    A*(nx) = λ*(nx). So (4/3,1) and (4,3) are the same eigenvector.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Confused with eigenvector
  1. Eigenvector proof (Replies: 4)

  2. Eigenvector Woes (Replies: 3)

Loading...