{
  "abstract": "In this article, we study the invertibility of matrices of the form $A+EDF$, where $A$ and $D$ are square matrices over a unital, not necessarily commutative, ring and $A$ is singular. Under natural hypotheses on kernels and images, we prove that $A+EDF$ is invertible if and only if $D$ is invertible, and obtain an explicit formula for the inverse of $A+EDF$ by purely algebraic methods. When the coefficient ring is stably finite, or more specifically a field, we obtain an invertibility criterion under weaker hypotheses. Our results extend and sharpen a theorem of Eriksson and Nordqvist for complex matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01948",
  "author_total": 1,
  "authors": [
    {
      "name": "Johan Öinert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60x9d6ccknhmw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01948",
  "fulltext_url": null,
  "id": "60x9d6ccknhmw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01948",
  "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": "W7216457257",
  "pdf_url": "https://arxiv.org/pdf/2610.01948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60x9d6ccknhmw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Invertibility of structured perturbations of singular matrices over unital rings",
  "title_text": "Invertibility of structured perturbations of singular matrices over unital rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/60x9d6ccknhmw",
  "venue": "arXiv",
  "versions": []
}