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Diagonalize matrix: please check work

  1. Apr 15, 2014 #1

    939

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    1. The problem statement, all variables and given/known data

    I am pretty sure I went completely wrong but not sure where. Please help!

    2 -3
    2 -5

    2. Relevant equations

    2 -3
    2 -5

    3. The attempt at a solution

    (note: I apologize for poor notation)

    eigenvalues = -4, 1
    eigenvectors = (1/√5)(1/2), (1/√10)(3/1)

    The matrix is not symmetric, thus the diagonal is (Q^-1)(A)(Q) = λ

    Без імені.jpg
     
    Last edited: Apr 15, 2014
  2. jcsd
  3. Apr 15, 2014 #2

    HallsofIvy

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    What you have done looks good but your last line is not at all clear. You have not said what "Q" is. [itex]Q^{-1}AQ[/itex] is a 2 by 2 matrix, not a "diagonal", and you have not said what "[itex]\lambda[/itex]" is intended to mean. Your attachment is correct.
     
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