Stuck with eigenvectors.

1. Apr 6, 2005

mprm86

The eigenvalues of the matrix $$\left(\begin{array}{cc}0 & \frac{1}{2}\\\frac{1}{2} & 0\end{array}\right)$$ are $\lambda_1 = \frac{1}{2}$ and $\lambda_2 = -\frac{1}{2}$
The problem here is that I have no idea of how to calculate the eigenvectors. Could some one please explain me, in detail, how do I find the eigenvectors?