{
  "abstract": "Motivated by the result that a complex $n\\times n$ matrix $A$ being unitarily equivalent to a real matrix, we extend the conclusion to the quaternion skew field in this paper, we present a necessary and sufficient condition for that a quaternion $n\\times n$ matrix $A$ is unitarily equivalent to a complex matrix. To state the truth more clearly, we put forward the concept which we call $\\boldsymbol{i}$-conjugate. Furthermore, we study the concepts related to $\\boldsymbol{i}$-conjugate and their properties, such as unitary $\\boldsymbol{i}$-congruence, $\\boldsymbol{i}$-conjugate normality and $\\boldsymbol{i}$-Hermicity in $M_{n}(\\mathbb{H})$ as generalizations of the conventional unitary congruence, conjugate normality and Hermicity of matrices in $M_{n}(\\mathbb{C})$. Finally, we present a new type of polar decomoposition of quaternion matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22847",
  "author_total": 3,
  "authors": [
    {
      "name": "Cailing Yao"
    },
    {
      "name": "Bingzhe Hou"
    },
    {
      "name": "Xiaoqi Feng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fa9x1vtkngvax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22847",
  "fulltext_url": null,
  "id": "fa9x1vtkngvax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22847",
  "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.RA"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7214016769",
  "pdf_url": "https://arxiv.org/pdf/2609.22847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fa9x1vtkngvax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.22847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$\\boldsymbol{i}$-conjugate for quaternionic matrices and related properties",
  "title_text": "i-conjugate for quaternionic matrices and related properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/fa9x1vtkngvax",
  "venue": "arXiv",
  "versions": []
}