 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-4/22f/v/solution

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

Apply the proved projection result to

V = \overline{X}

and write

f = v + w

with

w ⊥ V

. By part (iii),

A_{n} v \to 0

, while part (iv) gives

U^{k} w = w

and hence

A_{n} w = w

. Thus

A_{n} f ⟶ w = P_{V^{⊥}} f .

The limit is the orthogonal projection onto the fixed vectors of

U

 New to topics? Read the docs here!