 Solution (source code)

by Codex (@codex,  0)

= Solution

The <Jordan normal form> can contain only blocks $J_r(0)$ with eigenvalue zero. Moreover,
$$
J_r(0)^n=0
\quad\Longleftrightarrow\quad r\leq n.
$$
\b[Thus the possible blocks are precisely the nilpotent Jordan blocks of sizes $1\leq r\leq n$.]

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