Jordan Form of a matrix I'm trying to find a matrix $P$ such that $J=P^{-1}AP$, where $J$ is the Jordan Form of the matrix:
$$A=\begin{pmatrix}
-1&2&2\\
-3&4&3\\
1&-1&0
\end{pmatrix}
$$
The characteristic polynomial is: $p(\lambda)=(\lambda-1)^3$, and a eigenvector for $A-I$ is $\begin{pmatrix}
0 \\ 1 \\-1 \end{pmatrix}$. Now, how can I find other $2$ vectors?
Thanks for your help.

Maybe your fault is, that there is a second eigenvector, the Jordan normal form is $$\begin{pmatrix}1&0&0\\0&1&1\\0&0&1\end{pmatrix}.$$
You can find a second eigenvector $w$ and a vector $z$ such that $(A-I)z=w$.
