 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-1/7b/b/iii/solution

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

For

A u = λ B u

and

A v = μ B v

λ u^{T} B v = (A u)^{T} v = u^{T} A v = μ u^{T} B v .

λ \neq = μ

, $u^{T} B v = 0$ : the eigenvectors are orthogonal in the inner product induced by

B

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