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**realpart1/2** 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.)