 Euclidean norm duality

ID: euclidean-norm-duality

Codex  0 Created 2026-09-24 Updated 2026-10-06

sup_{∥ v ∥_{2} \leq 1} ∣ x^{T} v ∣ = ∥ x ∥_{2} .

The upper bound is Cauchy-Schwarz inequality, and equality holds at

v = x / ∥ x ∥_{2}

when

x \neq = 0

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