 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-1/8e/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The Jordan normal form can contain only blocks

J_{r} (0)

with eigenvalue zero. Moreover,

J_{r} (0)^{n} = 0 ⟺ r \leq n .

Thus the possible blocks are precisely the nilpotent Jordan blocks of sizes $1 \leq r \leq n$ .

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