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Finding the eigenvectors (and behavior of solution) around the

  1. Sep 23, 2008 #1
    finding the eigenvectors (and behavior of solution) around the critical points found in this thread: https://www.physicsforums.com/showthread.php?t=258349&referrerid=110346

    [tex]D_{f} = \[\begin{pmatrix}32x & 18y \\ 32x & -32y\end{pmatrix}\][/tex]

    [tex]D_{f}(1,1) = \[\begin{pmatrix}32 & 18 \\ 32 & -32\end{pmatrix}\] [/tex]

    [tex]= \[\begin{pmatrix}16 & 9 \\ 16 & -16 \end{pmatrix}\][/tex]

    [tex]det(A-\lambda I) =\[\begin{pmatrix} 16-\lambda & 9 \\ 16 & -16- \lambda \end{pmatrix}\] [/tex]

    [tex] = -256 + \lambda^{2} - 146 \ => \ \lambda = ^{+}_{-}20 [/tex]

    [tex] \lambda_{1} = 20: [/tex]

    [tex] (A-\lambda_{1} I)\xi^{(1)} = 0 \ => \ \[\begin{pmatrix} -4 & 9 \\ 16 & -36 \end{pmatrix}\]\xi^{(1)} = 0 [/tex]

    I can't get LaTeX to cooperate with me, that's supposed to say [-4 9; 16 -36]ξ(1) = 0

    [tex] => \ \xi^{(1)} = \left[^{9}_{4} \right] [/tex]

    Having trouble finding [tex] \xi^{(2)}[/tex] when [tex]\lambda_{2} = -20 [/tex].

    Keeps coming out to be [0 0]T.

    Any suggestions?
     
  2. jcsd
  3. Sep 24, 2008 #2
    Re: Eigenvectors

    Looks like you can't reduce the matrix before you do det(A - tI). Figured it out; thanks for looking.
     
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