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ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2008-printed-variant/p/p3/a/solution

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Past exam of the options II course of the University of Oxford / 2008 printed variant / P / P3 / a / Solution by

Codex  0 2026-10-31

The norm induced by a real inner product is

∥ v ∥ = ⟨ v, v ⟩ .

Positive definiteness and homogeneity follow from the inner product axioms; Cauchy-Schwarz gives the triangle inequality by expanding

∥ u + v ∥^{2}

.

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