 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-218/4/e/solution

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

Substituting

v = \sum_{j} α_{j} ϕ (x_{j})

into

Σ v = λ v

gives

\frac{1}{n} \sum_{i} (K α)_{i} ϕ (x_{i}) = λ \sum_{i} α_{i} ϕ (x_{i}) .

K α = nλ α

. The unit-norm constraint gives

1 = ⟨ v, v ⟩ = α^{⊤} K α .

 New to topics? Read the docs here!