 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-225/3/ii/solution

Codex  0 Created 2026-09-28 Updated 2026-10-03

Because

C_{i} = L_{i} L_{i}^{*}

∥ L_{i} ∥_{HS}^{2} = tr (L_{i} L_{i}^{*}) = tr C_{i} < \infty.

∥ L_{2}^{*} L_{1} ∥_{1} \leq ∥ L_{2} ∥_{HS} ∥ L_{1} ∥_{HS} < \infty.

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