{
  "abstract": "We classify all real linear into preservers of semipositivity on $M_{m,n}(\\mathbb{R})$, $m,n\\ge2$, for arbitrary source and target pairs of proper cones, without assuming invertibility or a prescribed form. The classification consists of product maps $L(A)=XAY$ and degenerate maps $L(A)=Ψ(u^TA)$, subject to explicit necessary and sufficient cone conditions. For square minimal semipositivity with respect to the standard nonnegative orthant, preservation instead forces the operator to be invertible: for $n\\ge2$, the linear into preservers are exactly the maps $L(A)=XAY$ and $L(A)=XA^TY$ with $X,Y$ invertible and $X^{-1},Y^{-1}\\ge0$. We also classify all linear preservers of orthant semipositivity from $M_{2,2}(\\mathbb{R})$ to $M_{1,3}(\\mathbb{R})$ into three disjoint classes, two of which lie outside product form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27413",
  "author_total": 2,
  "authors": [
    {
      "name": "Yulong Tian"
    },
    {
      "name": "Jinli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65gms1nsvhe07.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27413",
  "fulltext_url": null,
  "id": "65gms1nsvhe07",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27413",
  "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",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7223147828",
  "pdf_url": "https://arxiv.org/pdf/2610.27413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65gms1nsvhe07.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.27413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Linear Preservers of Semipositivity and Minimal Semipositivity",
  "title_text": "Linear Preservers of Semipositivity and Minimal Semipositivity",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/65gms1nsvhe07",
  "venue": "arXiv",
  "versions": []
}