 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ib/paper-1/1e/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

True. If

A v = λ v

with

v \neq = 0

and

A = A^{*}

, then

λ v^{*} v = v^{*} A v = (v^{*} A v)^{*} = \overset{ˉ}{λ} v^{*} v .

Since

v^{*} v > 0

λ = \overset{ˉ}{λ}

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