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Eigenvector of 2x2 matrix

  1. Mar 8, 2012 #1
    for the matrix
    {5,0}
    {2,-2}

    when determining the eigenvector for its 2nd eigenvalue, -2, you would start out by doing


    {5--2 ,0}
    {2 ,-2--2}

    giving

    {7,0}
    {2,0}

    In equation form this is

    7u + 0v = 0
    2u + 0v = 0

    Ordinarily I would set u or v to a value and solve for the other letter.


    But in this case this can't be done since in both equations v has a coefficient of 0.


    So what would you do in this situation?
     
  2. jcsd
  3. Mar 8, 2012 #2

    phyzguy

    User Avatar
    Science Advisor

    Clearly u=0, and the equations will both be satisfied for any value of v, so the normalized eigenvector is (0,1).
     
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