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Math Help - System of DiffEq Problem!

  1. #1
    Mec
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    System of DiffEq Problem!

    Hey guys,

    First time poster here, love the site so far though. Thanks in advance for any help received. I'm really lost!

    I'm doing a very simple system of differential equations problem here and I've run into a situation I don't know how to handle.

    The differential equation is:

    x' = \left(\begin{array}{cc}1&i\\-i&1\end{array}\right) x

    Now, I have the eigenvalues as 0 and 2. Two distinct real eigenvalues, should be easy, right!?

    But my eigenvectors are complex... Namely:

    E_0 = \left(\begin{array}{cc}-i\\1\end{array}\right)

    E_2 = \left(\begin{array}{cc}i\\1\end{array}\right)


    (Complex conjugates as expected with complex eigenvectors)


    So how do I handle that? I don't know how to get a solution with real eigenvalues and complex eigenvectors... Help please!
    Last edited by Mec; April 22nd 2010 at 02:58 PM.
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  2. #2
    Mec
    Mec is offline
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    Hi, just wanted to give this a friendly bump because I feel like its a rather simple answer that I'm missing.

    For example, is it possible that the answer is unaffected by the complex eigenvectors?

    Therefore, y = c_1 \left(\begin{array}{cc}-i\\1\end{array}\right) e^{0t} + c_2 \left(\begin{array}{cc}i\\1\end{array}\right) e^{2t}



    Does that look correct?
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