 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2012/ia/paper-1/8b/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-07

P^{T} P = I

. Consequently

(P u) \cdot (P v) = u^{T} P^{T} P v = u^{T} v = u \cdot v .

Thus it preserves every real inner product, and in particular lengths and angles.

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