 Solution

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

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

ϕ v = μv

for a nonzero eigenvector

v

, then

0 = ϕ^{n} v = μ^{n} v .

Hence every eigenvalue satisfies $μ = 0$ . Since a complex endomorphism has an eigenvalue, zero is the only possible eigenvalue.

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