Jordan Normal Form quick help!!!
I have two matricies A and B:
$\displaystyle A=\left[\begin{array}{ccc}
0 & 0 & 1\\
1 & 0 & -3\\
0 & 1 & 3\end{array}\right]$ $\displaystyle B=\left[\begin{array}{ccccc} 3 & 1 & 0 & 1 & -2\\
1 & 3 & -1 & 0 & 1\\
-1 & -1 & 4 & 3 & -3\\
1 & 1 & -1 & 2 & 1\\
-2 & -2 & 2 & 2 & 1\end{array}\right]
$
which I need to put in Jordan Normal Form:
$\displaystyle J_{A}=\left[\begin{array}{ccc}
-1 & 0 & 0\\
0 & 1 & 1\\
0 & 0 & 1\end{array}\right]$ $\displaystyle J_{B}=\left[\begin{array}{ccccc}
2 & 1 & 0 & 0 & 0\\
0 & 2 & 0 & 0 & 0\\
0 & 0 & 3 & 1 & 0\\
0 & 0 & 0 & 3 & 1\\
0 & 0 & 0 & 0 & 3\end{array}\right]$
(Not sure if I got this right)
and then (my biggest problem) construct matrices S an T so that
$\displaystyle S^{-1}AS=J_{A}$ and $\displaystyle T^{-1}BT=J_{B}$ (I know th significance, but I'm not sure how to construct these matricies.)