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Thread: Generalized eigenvector?

  1. #1
    Apr 2009

    Generalized eigenvector?

    The problem I'm doing asks me to solve the normal system x'=Ax, but A is an unknown 2x2 matrix. However, I'm given some initial values and:

    A \left(\begin{array}{r}-1\\4\end{array}\right) = -4 \left(\begin{array}{r}-1\\4\end{array}\right)

    OK, I know this says -4 is an eigenvalue with corresponding eigenvector (-1,4)

    A \left(\begin{array}{r}0\\1\end{array} \right) = -4 \left(\begin{array}{r}0\\1\\\end{array} \right)
    + \left( \begin{array}{r}-1\\4\end{array}\right)

    But I'm not sure what to make of this.

    My current approach is to find $\displaystyle e^{At} $ so I need a second, maybe generalized? eigenvector and corresponding eigenvalue.

    edit: Never mind, I figured I can just solve for A
    Attached Thumbnails Attached Thumbnails Generalized eigenvector?-question-4.jpg  
    Last edited by cubrikal; May 13th 2009 at 09:55 PM. Reason: solved
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