 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/8b/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

U

U^{†} U = U U^{†} = I .

Uv = λ v

with

v \neq = 0

, unitarity preserves norms, so

∥ v ∥ = ∥ Uv ∥ = ∥ λ v ∥ = ∣ λ ∣ ∥ v ∥.

Therefore every eigenvalue satisfies

∣ λ ∣ = 1 .

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