Making Jordan Canonical Form: Box in Bottom Lambdas

[Dustinsfl]

I am trying to make this into jordan canonical form.

How can I box in the bottom two lambdas?

$$
\left[\begin{array}{ccc}
\begin{array}{cccc|}
\lambda & 1 & 0 & \\
& \lambda & 1 & 0\\
& & \lambda & 1\\
& & & \lambda\\\hline
\end{array}
& & \\
& \begin{array}{c|}
\lambda\\\hline
\end{array} & \\
& & \begin{array}{c|}
\lambda\\\hline
\end{array}
\end{array}\right]
$$

On my pdf, it doesn't do this.

 

[Ackbach]

Why not just do this sort of thing:

$$\left[\begin{array}{cc}\boxed{\lambda} & \\ &\boxed{\lambda}\end{array}\right]$$

Anything you want can be in a boxed environment, including another array environment. Also note that entries in the array environment can be empty. With that combination of information, I think you can do what you want with boxing.