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Linear algebra eigen vector

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data
    im trying to find the eigen vector for these 2 matrices: A=[0,0;0,8] AND A=[-8,0;0,0]


    2. Relevant equations



    3. The attempt at a solution
    BACICALLY WHAT IM DOING IS "GUESSING" AT What x1, is then im coming up wth the solution to x2 once ive made my guess for x1. how can i know for sure if my guyess is correct?
     
  2. jcsd
  3. Dec 6, 2009 #2

    Pengwuino

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    Gold Member

    What do you mean by your guesses? Finding eigenvectors and eigenvalues is a process that doesn't need guessing.
     
  4. Dec 6, 2009 #3

    HallsofIvy

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    Staff Emeritus
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    Also what do you mean by "the eigenvector for these matrices". Each matrix has two (obvious) eigenvalues and an infinite number of eigenvectors. Do you mean "find the eigenvectors of each matrix" or "find a vector that is an eigenvector for both matrices"?
     
  5. Dec 6, 2009 #4
    I mean find the eigenvectors of each matrix. The original question is Find the eigenvals and eigenvecs of A=[1,0;0,9]. I know the eigvals are 1 and 9. However when I try to find the eigvec for lamda =1 and lamda = 9 respectively i get these matrices: when lamda =1 [0,0;0,8] and lamda =9 [-8,0;0,0]. For some reason I'm just thinking that eigenvector for both of these is 0 becase for instance in the mathrix when lamda =1 you get the eqn:
    0x+8y=0 and 0x+0y=0. This is almost the same case for when lamda = 9. How do you find x and y to get the eigenvectors without them being 0 because there is no such thing as a 0 eigenvector.
     
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