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Mathematicians prove sharp norm inequality using linear algebra

A new paper published on arXiv presents a concise linear-algebraic proof for a fundamental norm inequality in mathematics. The inequality, which relates the L1, L-infinity, and L2 norms of a vector in R^n, has applications in optimization and numerical analysis. The proof method, which leverages determinants of quadratic forms, also extends to proving Buzano's inequality for real vectors, with the derived constant shown to be optimal. AI

RANK_REASON The cluster contains a single academic paper detailing a mathematical proof. [lever_c_demoted from research: ic=1 ai=0.1]

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Mathematicians prove sharp norm inequality using linear algebra

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  1. arXiv cs.LG TIER_1 English(EN) · Jose Antonio Lara Benitez ·

    A Sharp Norm Inequality and Buzano's Inequality via Determinants

    arXiv:2604.01525v2 Announce Type: replace-cross Abstract: We give a short linear-algebraic proof of the inequality $$ \|x\|_1\,\|x\|_\infty \le \frac{1+\sqrt{n}}{2}\,\|x\|_2^2, $$ valid for every $x\in\mathbb{R}^n$. This inequality relates three fundamental norms on finite-dimens…