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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:


    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


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    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.
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