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Please help me calculate the Eigen vectors of this matrix.
$\begin{pmatrix} 3 & 0 & 1\\ 1 & 3 & 0\\ 0 & 1 & 3 \end{pmatrix}$

The first vector comes out to be null, no clue how to find out the other two.

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    Thanks alot, I often get confused with Eigen-value problems. I have a few other questions too, if you guys dont mind :)2012-12-21

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Try $v_1=(1,1,1)^T$, $v_2=(1-i\sqrt{3},-2,1+i\sqrt{3})^T$, $v_3 = \overline{v_2}$.

$A v_i = \lambda_i v_i$, where $A$ is the matrix above and $\lambda_i$ can be found by solving $\lambda^3-9\lambda^2+27 \lambda -28 = 0$. (By inspection, $4$ is a solution, and synthetic division results in $x^2-5x+7=0$.)

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    @RobertIsrael: Fixed. Thanks!2012-12-21