{
  "abstract": "The following inequality for vectors $\\mathbf{v}, \\mathbf{w} \\in \\mathbb{R}^n$ was considered in [Linear and Multilinear Algebra 74:1779--1798 (2026)]: \\[\\|\\mathbf{v}^p\\|\\|\\mathbf{w}^p\\| - \\langle\\mathbf{v}^p,\\mathbf{w}^p\\rangle \\leq \\|\\mathbf{v}\\|^p\\|\\mathbf{w}\\|^p - \\langle\\mathbf{v},\\mathbf{w}\\rangle^p,\\] where $\\mathbf{v}^p$ is the vector that is obtained by raising each entry of $\\mathbf{v}$ to the power $p$. It was shown that this inequality holds for all positive integers $p$, and it was conjectured that it holds for all real $p \\geq 2$ when the entries of $\\mathbf{v}$ and $\\mathbf{w}$ are positive. A formula for the maximum amount by which the inequality's right-hand side can exceed its left-hand side for nonnegative unit vectors was also conjectured. We prove both of these conjectures, and we determine exactly when the inequality holds with equality. We also present a new generalization of this inequality to three or more vectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12063",
  "author_total": 2,
  "authors": [
    {
      "name": "Nathaniel Johnston"
    },
    {
      "name": "Mohammad Sababheh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15m0akafbexa8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12063",
  "fulltext_url": null,
  "id": "15m0akafbexa8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12063",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7221171928",
  "pdf_url": "https://arxiv.org/pdf/2610.12063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15m0akafbexa8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hadamard powers of Gram matrices and Generalized Cauchy-Schwarz inequalities",
  "title_text": "Hadamard powers of Gram matrices and Generalized Cauchy-Schwarz inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/15m0akafbexa8",
  "venue": "arXiv",
  "versions": []
}