A Determinantal Approach to a Sharp $\ell^1-\ell^\infty-\ell^2$ Norm Inequality
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908933091753984 |
|---|---|
| author | Benitez, Jose Antonio Lara |
| author_facet | Benitez, Jose Antonio Lara |
| contents | We give a short linear--algebraic proof of the inequality \[ \|x\|_1\,\|x\|_\infty \le \frac{1+\sqrt{p}}{2}\,\|x\|_2^2, \] valid for every \(x\in\mathbb{R}^p\). 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 $(1+\sqrt{p})/2$ is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Determinantal Approach to a Sharp $\ell^1-\ell^\infty-\ell^2$ Norm Inequality Benitez, Jose Antonio Lara Classical Analysis and ODEs Machine Learning History and Overview Optimization and Control We give a short linear--algebraic proof of the inequality \[ \|x\|_1\,\|x\|_\infty \le \frac{1+\sqrt{p}}{2}\,\|x\|_2^2, \] valid for every \(x\in\mathbb{R}^p\). 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 $(1+\sqrt{p})/2$ is optimal. |
| title | A Determinantal Approach to a Sharp $\ell^1-\ell^\infty-\ell^2$ Norm Inequality |
| topic | Classical Analysis and ODEs Machine Learning History and Overview Optimization and Control |
| url | https://arxiv.org/abs/2604.01525 |