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Eigenvalues and vectors - finding original matrix

  1. Dec 11, 2007 #1
    How do I determine what the original matrix was that yielded these two eigenvalues with the corresponding eigenvectors:

    [tex]\lambda_1 = -3[/tex] Eigenvector: [0,1]

    [tex]\lambda_2 = 2[/tex] Eigenvector: [1,0]

    I've played around with det(A-lambda I) but can't find the matrix! I even just did some trial and error matrices in Maple trying to figure it out. If anyone can find me the matrix I'd be very impressed.
  2. jcsd
  3. Dec 11, 2007 #2


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    Homework Helper

    Well if you have the eigenvectors of a matrix A then A can be represented as:
    where D is a diagonal matrix with the diagonal elements as [itex]\lambda_1 \ and \ \lambda_2[/itex]

    and P is the eigenvectors of the eigenvalues....

    so from your problem:

    D would be the matrix:
    [-3 0]
    [0 2]

    and the first column for P would be the eigenvector for -3 and the 2nd column would be the eigenvector for 2...so you now have P..find P[itex]^{-1}[/itex] and multiply out
  4. Dec 11, 2007 #3


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    Gold Member

    What does the matrix
    a11 a12
    a21 a22

    map (1,0) and (0,1) to?
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