{
  "abstract": "We study unitary similarity of dual complex matrices and dual quaternion matrices. First, we characterize unitary similarity in terms of the existence of a skew-Hermitian solution to a Sylvester-type matrix equation. For $2\\times2$ dual complex matrices, we obtain a complete three-trace criterion when the standard part is nonnormal and analyze the limitations of trace-word criteria when the standard part is normal. We then prove, for every $n\\geq1$, that two $n\\times n$ dual quaternion matrices are unitarily similar if and only if their dual complex adjoint matrices are unitarily similar, and we extend this result to finite families. As a scalar consequence, we derive a finite Trace-word criterion when the standard part is nonreal and exhibit its failure when the standard part is real.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30060",
  "author_total": 3,
  "authors": [
    {
      "name": "Cailing Yao"
    },
    {
      "name": "Bingzhe Hou"
    },
    {
      "name": "Xiaoqi Feng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a0k486eem0f3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30060",
  "fulltext_url": null,
  "id": "1a0k486eem0f3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30060",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7223221924",
  "pdf_url": "https://arxiv.org/pdf/2610.30060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a0k486eem0f3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.30060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unitary similarity for dual complex matrices and dual quaternion matrices",
  "title_text": "Unitary similarity for dual complex matrices and dual quaternion matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/1a0k486eem0f3",
  "venue": "arXiv",
  "versions": []
}