= Solution
Write $J_r(\lambda)$ for a size-$r$ <Jordan block>. The <characteristic polynomial> fixes the total dimensions at $2$ and $-7$, while the <minimal polynomial> fixes the largest <Jordan block> at each <eigenvalue>. Consequently, the blocks for $2$ have total size four, largest size two, and at least one size-two block. The blocks for $-7$ both have size one. \b[The complete list, up to similarity, is]
$$
\boxed{\operatorname{diag}(J_2(2),J_2(2),-7,-7),\qquad \operatorname{diag}(J_2(2),2,2,-7,-7),\quad J_2(2)=\begin{pmatrix}2&1\\0&2\end{pmatrix}.}
$$
These <Jordan normal forms> are inequivalent because their $2$-<eigenspaces> have different dimensions, two and three.
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