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Math Help - General solution for a matrix with 1 real and two complex eigen values.

  1. #1
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    {SOLVED}General solution for a matrix with 1 real and two complex eigen values.

    Hey guys, I was hoping you could help with a problem I'm having.
    I found from my 3x3 matrix 3 eigenvalues where one is real and the other two are complex. I don't know how to express the general solution for this though and it is the first time I've tried to solve for the GS of a 3x3.
    the eiegen vectors are
    v_1 = (1, 0, 0)
    v_2 = (5/26+i/26, -1/2+i/2, 1)
    v_3 = (5/26-i/26, -1/2-i/2, 1)
    I haven't put the into vector column form yet but that's pretty straight forward.
    Any help is appreciated,
    Thanks!
    Last edited by issacsh413; September 9th 2012 at 03:05 PM.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: General solution for a matrix with 1 real and two complex eigen values.

    What is original matrix?
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  3. #3
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    Re: General solution for a matrix with 1 real and two complex eigen values.

    Quote Originally Posted by MaxJasper View Post
    What is original matrix?

    [(3,0,-1),(0,-3,-1),(0,2,-1)]

    the eigen values were 3, (-2+i), and (-2-i).

    I tried using (c_1)*(e^3t)[1,0,0]+(c_2)(e^-2t)[cos(t)(v_2)-sin(t)(v_3)]+(c_3)(e^-2t)[sin(t)(v_2)+cos(t)(v_3)]

    which is the GS for a real rood plus the GS for 2 complex roots in a 2x2 matrix.

    It is incorrect though.
    Last edited by issacsh413; September 9th 2012 at 02:22 PM.
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