Can one eigenvalue have two different eigenvectors?

I think the answer is no, but to be precise, is it correct to assume that if we have one eigenvalue that is the same, then the eigenvectors for these have to be the same too?

For example,

$$\begin{gathered}
T(1,0,0) = (0, - 2,0) \hfill \\
T(0,1,0) = (0,0.5,0) \hfill \\
T(0,0,1) = (0,1.5,0) \hfill \\
\end{gathered}$$

The transformation matrix $T$ has two eigenvalues that are zero, but this cannot be the case? The other one is $0.5$.