 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-3/15c/c/solution

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

Uv = λ v

with

v \neq = 0

, unitarity gives

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

Hence $∣ λ ∣ = 1$ . Every eigenvalue of a unitary matrix therefore lies on the unit circle.

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