{
  "abstract": "The real stability radius problem asks for the smallest real perturbation that makes a given matrix lose rank, and it is a structured counterpart of the corresponding complex stability radius problem. In this paper, we consider an angular version of this question for sectorial matrices, where the size of a perturbation is measured by its largest phase instead of its largest singular value. More precisely, for a sectorial matrix $M$, we investigate the minimum required largest phase of a real and sectorial perturbation $Δ$ for which $I+MΔ$ loses rank. We show that for some matrices, the complex and the real angular stability radius are the same, but that they are in general different, such as when $M$ is diagonal or complex symmetric. For these cases, we derive a formula for the real angular stability radius, and this formula depends on the two largest phases of $M$. Moreover, in these cases we show that the result for $n \\times n$ matrices can be reduced to that for $2 \\times 2$ matrices by compressing an arbitrary real destabilizing perturbation to the real two-dimensional subspace spanned by the real and imaginary parts of a destabilizing vector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30843",
  "author_total": 4,
  "authors": [
    {
      "name": "Sei Zhen Khong"
    },
    {
      "name": "Xin Mao"
    },
    {
      "name": "Li Qiu"
    },
    {
      "name": "Axel Ringh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bafchs0vah5a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30843",
  "fulltext_url": null,
  "id": "2bafchs0vah5a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30843",
  "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.OC"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7204955446",
  "pdf_url": "https://arxiv.org/pdf/2608.30843",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bafchs0vah5a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30843",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30843"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the real angular stability radius for sectorial matrices",
  "title_text": "On the real angular stability radius for sectorial matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/2bafchs0vah5a",
  "venue": "arXiv",
  "versions": []
}