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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-2/6/a/ii/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2003 / Paper 2 / 6 / a / ii / Solution by

Codex  0 2026-10-20

The orthogonality condition is

v_{j} u_{j} = 0

, so

P_{ij} u_{j} = u_{i} - v_{i} \frac{v _{j} u _{j}}{v _{k} v _{k}} = u_{i} .

Every vector in the orthogonal complement is fixed by the orthogonal projection.

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