{
  "abstract": "In the setting of a hyperbolic (polynomial) system $(\\mathcal{V}, p, e)$ of degree $n$, an $n$-tuple $\\mathbf{A} = \\big[ a_1, a_2, \\dots, a_n \\big]$ is said to be an $e$-doubly stochastic $\\mathcal{V}$-matrix if each $a_i$ belongs to the hyperbolicity cone, has trace $1$, and $a_1 + a_2 + \\dots + a_n = e$. In this article, we characterize linear preservers of such $\\mathcal{V}$-matrices, describe some connections between $e$-doubly stochasticity and majorization, and study extreme points of the set of all $e$-doubly stochastic $\\mathcal{V}$-matrices. We show, for example, that $(i)$ when $n>1$, positive, unital, and trace-preserving transformations are (the only) linear transformations on $\\mathcal{V}$ that preserve $e$-doubly stochasticity; $(ii)$ when $\\mathbf{A}$ is $e$-doubly stochastic, the eigenvalue vector of the linear combination $\\sum_{i=1}^{n} r_ia_i$ is majorized by the coefficient vector $(r_1, r_2, \\dots, r_n)^{T} \\in \\mathbb{R}^n$; and $(iii)$ when $p$ is complete, $e$-doubly stochastic $\\mathcal{V}$-matrices induced by (generalized) Jordan frames are extreme points of the compact convex set of all $e$-doubly stochastic $\\mathcal{V}$-matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32349",
  "author_total": 3,
  "authors": [
    {
      "name": "Juyoung Jeong"
    },
    {
      "name": "M. Seetharama Gowda"
    },
    {
      "name": "Sudheer Shukla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eq31rjayh3ng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32349",
  "fulltext_url": null,
  "id": "5eq31rjayh3ng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32349",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7214758929",
  "pdf_url": "https://arxiv.org/pdf/2609.32349",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eq31rjayh3ng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32349",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32349"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On $e$-doubly stochastic matrices over hyperbolic (polynomial) systems",
  "title_text": "On e-doubly stochastic matrices over hyperbolic (polynomial) systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5eq31rjayh3ng",
  "venue": "arXiv",
  "versions": []
}