{
  "abstract": "In this paper, zeon matrix groups are discussed for the first time. Extending the concept of unitary complex matrices (i.e., matrices $A$ such that $A^\\dagger A=\\mI$) to matrices having entries in the complex zeon algebra $\\CZ$, a ``zeon dagger'' operator $\\zdag$ is defined and used to declare a zeon matrix $Ξ$ to be {\\em unitary} if $Ξ^\\zdagΞ=\\mI$. The unitary zeon matrices of order $n$ form a subgroup $\\U_n$ of all invertible order-$n$ zeon matrices. A more interesting notion is that of ``weak unitarity'' of a zeon matrix. In particular, a zeon matrix $Ξ$ will be said to be {\\em weakly unitary} if $Ξ^\\zdagΞ=\\mI+Γ$, where $Γ$ is a diagonal nilpotent zeon matrix. The weakly unitary matrices of order $n$ form a group $\\W_n$, of which $\\U_n$ is a subgroup. It is further shown that the exponential of a graph's nilpotent adjacency matrix has a natural orthogonal decomposition into the sum of a weakly unitary zeon matrix and a nilpotent zeon matrix. Eigenvalues of the weakly unitary zeon matrix reveal information about the graph's cycles and paths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33891",
  "author_total": 1,
  "authors": [
    {
      "name": "G. Stacey Staples"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1g922yfqw4rqt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33891",
  "fulltext_url": null,
  "id": "1g922yfqw4rqt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33891",
  "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.OA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7223860973",
  "pdf_url": "https://arxiv.org/pdf/2610.33891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1g922yfqw4rqt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weakly Unitary Zeon Matrices",
  "title_text": "Weakly Unitary Zeon Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1g922yfqw4rqt",
  "venue": "arXiv",
  "versions": []
}