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Math Help - Eigen values?

  1. #1
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    Eigen values?

    Hi,

    I am totally lost in how I am meant to solve this.

    I have to find the eigen values of the matrix

    \left[\begin{array}{cc}1&1\\1&2\end{array}\right]

    I then find det(B - \lambda I) = \left[\begin{array}{cc}1 - \lambda &1\\1&2 - \lambda \end{array}\right]

    = (1 - \lambda )(2 - \lambda ) - (1\cdot1)

    From there it starts to get messy, I just want to know if I am doing anything wrong.
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  2. #2
    Junior Member piglet's Avatar
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    Quote Originally Posted by Beard View Post
    Hi,

    I am totally lost in how I am meant to solve this.

    I have to find the eigen values of the matrix

    \left[\begin{array}{cc}1&1\\1&2\end{array}\right]

    I then find det(B - \lambda I) = \left[\begin{array}{cc}1 - \lambda &1\\1&2 - \lambda \end{array}\right]

    = (1 - \lambda )(2 - \lambda ) - (1\cdot1)

    From there it starts to get messy, I just want to know if I am doing anything wrong.
    Explains very clearly how to do it here Eigenvalue algorithm - Wikipedia, the free encyclopedia
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  3. #3
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    You want the determinant to be zero so that you will have a nontrivial solution. Just expand your determinant function and set it equal to zero. You will only have to solve a quadratic equation.
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  4. #4
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    Carrying on with your method I get the eigen values to be \frac{3+\sqrt{5}}{2} and \frac{3-\sqrt{5}}{2}.

    For my set of eigen vectors I get \left[\begin{array}{c}-\frac{(1 + \sqrt{5})}{2}\\1  \end{array}\right] and the second to be \left[\begin{array}{c}\frac{1 + \sqrt{5}}{2}\\1  \end{array}\right]


    Can someone confirm this?

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  5. #5
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Beard View Post
    Carrying on with your method I get the eigen values to be \frac{3+\sqrt{5}}{2} and \frac{3-\sqrt{5}}{2}.

    For my set of eigen vectors I get \left[\begin{array}{c}-\frac{(1 + \sqrt{5})}{2}\\1  \end{array}\right] and the second to be \left[\begin{array}{c}\frac{1 + \sqrt{5}}{2}\\1  \end{array}\right]


    Can someone confirm this?

    correct
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