Research
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 xinR^n. This inequal
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 xinR^n. This inequality relates three fundamental norms on finite-dimensional spaces and has applications in optimization and numerical analysis. Our proof exploits the determinantal structure of a parametrized family of quadratic forms, and we show the constant (1+sqrt{n})/2$ is optimal. The inequality is a special case of Buzano's inequality, and the same method also proves Buzano's inequality for real vectors.
Source: arXiv cs.LG | 2026-09-28