$\textsf{Suppose that A is a matrix whose characteristic polynomial is}$

$$(\lambda-2)^2(\lambda + 1)^2,

\quad \dim\left(E_2\right)=1

\quad \dim\left(E_{-1}\right)=2$$

$\textsf{expanded form is }$

$$(\lambda-2)^2(\lambda + 1)^2

=\lambda^4 - 2 \lambda^3 - 3 \lambda^2 + 4 \lambda + 4$$

$$\begin{bmatrix}2&0&0&0\\0&2&0&0\\0&0&-1&0\\0&0&0&-1\end{bmatrix}

=(\lambda-2)^2(\lambda + 1)^2$$

$\textsf{Find the Jordan Normal Form of A}$

$\textsf{ok I have been looking thru examples but still don't understand what}$

$$\quad \dim\left(E_2\right)=1 \quad \dim\left(E_{-1}\right)=2$$.

$\textsf{is about.}$