On the n-th linear polarization constant of ℝⁿ

2022/08/10 by Damián Pinasco, Pinasco, Damian
Computer Science · Mathematics · #52A40 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Primary 46G25 #Secondary 26D05

paper · pdf · doi:10.48550/arxiv.2208.05584

openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that given any set of n unit vectors \v_i\_i=1ⁿ⊂ \mathbb Rⁿ, the inequality sup_\Vert x \Vert_{\mathbb Rⁿ} =1 \vert ⟨ x, v₁ ⟩ ⋯ ⟨ x, v_n⟩\vert ≥ n^-n/2 holds for n ≤ 14. Moreover, the equality is attained if and only if \v_i\_i=1ⁿ is an orthonormal system.

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