{
  "abstract": "In this paper, we introduce and study conformal permutation matrices. In particular, for a permutation $π_s\\in S_n$, we define the corresponding conformal permutation matrix $H_{π_s}$ and show that its $d-$th power, where $d=n/\\gcd(s,n)$, is a diagonal block matrix whose blocks are products of certain matrix blocks $h_i$. We further show that these diagonal blocks share a common subset of eigenvalues and prove that $H_{π_s}$ is block-diagonalizable. We also introduce the notion of conformal circulant matrix and investigate its eigenvalues. Finally, we establish a necessary and sufficient condition for a rectangular matrix to be conformal circulant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14736",
  "author_total": 2,
  "authors": [
    {
      "name": "Cristina Manzaneda"
    },
    {
      "name": "Enide Andrade"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwkcmrkpfdr6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14736",
  "fulltext_url": null,
  "id": "fwkcmrkpfdr6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14736",
  "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.CO"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7213232278",
  "pdf_url": "https://arxiv.org/pdf/2609.14736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fwkcmrkpfdr6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On properties of the conformal circulant matrices",
  "title_text": "On properties of the conformal circulant matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fwkcmrkpfdr6d",
  "venue": "arXiv",
  "versions": []
}