{
  "abstract": "Let $\\mathbb{D}$ be a division ring with an involution $x \\mapsto x^\\star$, and $n \\geq 2$ be an integer. Denote by $\\mathcal{H}_n(\\mathbb{D})$ the set of all $n$-by-$n$ Hermitian matrices with entries in $\\mathbb{D}$, and by $\\mathcal{A}\\mathcal{H}_n(\\mathbb{D})$ the set of all matrices $A-A^\\star$ with $A \\in \\mathcal{M}_n(\\mathbb{D})$. Here, we give a complete solution to the following problem: Determine all group homomorphisms from $\\mathcal{H}_n(\\mathbb{D})$ to $\\mathbb{D}^n$ (respectively, from $\\mathcal{A}\\mathcal{H}_n(\\mathbb{D})$ to $\\mathbb{D}^n$ unless $(-)^\\star$ is the identity) that take every matrix to a right linear combination of its columns. The solution to this problem was already known when $(-)^\\star$ is the identity, and the novelty here lies in the generalization to arbitrary involutions, and in particular in the noncommutative case. These results are to be used in a subsequent article on subspaces of Hermitian matrices of bounded rank, and on large spaces of diagonalisable matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20363",
  "author_total": 1,
  "authors": [
    {
      "name": "Clément de Seguins Pazzis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s1c7bvtp3g5c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20363",
  "fulltext_url": null,
  "id": "1s1c7bvtp3g5c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20363",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7213605155",
  "pdf_url": "https://arxiv.org/pdf/2609.20363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s1c7bvtp3g5c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Range-compatible homomorphisms on Hermitian matrices",
  "title_text": "Range-compatible homomorphisms on Hermitian matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/1s1c7bvtp3g5c",
  "venue": "arXiv",
  "versions": []
}