I've got the following matrix $A$ for an endorphism within a base $v_1, v_2, v_3$
$$ A = \left( \begin{array}{ccc} 0 & 0 & -1 \\ 1 & 0 & -3 \\ 0 & 1 & -3 \\ \end{array} \right) $$
I need to find the base vectors $v^'_1, v^'_2, v^'_3$ for which the matrix of this endorphism looks like follows (this is the Jordan matrix of this endorphism as I worked out)
$$ A^' = \left( \begin{array}{ccc} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & 0 & -1 \\ \end{array} \right) $$
So I know there must exist a matrix $T$ so that $AT = TA^'$. But how does this help to get the base vectors $v^'_1, v^'_2, v^'_3$ based on $v_1, v_2, v_3$?