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Finding the eigenvectors in triangular matrices

  1. May 3, 2012 #1
    I thought I would ask this in the homework section.

    1. The problem statement, all variables and given/known data
    I should be able to write down the eigenvectors and eigenvalues of diagonal and triangular matrices on sight.


    M = \begin{bmatrix}
    1 &0 \\[0.3em]
    0 & x \\[0.3em]

    \end{bmatrix}

    vs.

    M = \begin{bmatrix}
    -1 & -1 \\[0.3em]
    0 & x-(1/4) \\[0.3em]

    \end{bmatrix}





    2. Relevant equations



    3. The attempt at a solution

    Obviously, I can see in the diagonal matrix that eigenvalues are λ_1 =1 and λ_2 =x
    Therefore, the eigenvectors are e_1= (1 0) and e_2 =(0 1)

    Now for the triangular matrix: by sight, I can see λ_1 =-1 and e_1 = (1 0 )

    What I cannot do is figure out (by looking at the matrix) that if λ_2=x-(1/4) then e_2 = (-1 x+(3/4) ) Any help would be much appreciated. Thanks!
     
  2. jcsd
  3. May 3, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi eherrtelle59! :smile:

    (try using the X2 button just above the Reply box :wink:)
    -1*-1 + -1*(x+3/4) = (x - 1/4)*-1

    0*-1 + (x-1/4)*(x+3/4) = (x - 1/4)*(x+3/4)
     
  4. May 3, 2012 #3

    Mark44

    Staff: Mentor

    This looks very similar to a thread you started in one of the math technical sections (https://www.physicsforums.com/showthread.php?t=602860). It's slightly different, so I'm just going to advise you that homework and homework-like questions belong here, not in the math technical section.
     
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