{
  "abstract": "The zero-trace index $t(A)$ of a square complex matrix $A$ is introduced. It is defined as the largest integer $k$ such that $A$ admits a $k \\times k$ compression with trace zero. This concept is analogous to the zero-dilation index $d(A)$ and is closely related to the $k$-numerical range. The $k$-numerical range is characterized as an intersection of half-planes, which is used to derive a formula for $t(A)$ that reduces its computation to the Hermitian case. Conditions for $t(A) = d(A)$ are also established, and matrices satisfying $t(A) = n - 1$ are characterized. Finally, the zero-trace index is determined for several classes of matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24486",
  "author_total": 2,
  "authors": [
    {
      "name": "Kennett L. Dela Rosa"
    },
    {
      "name": "Eloise P. Misa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7wm6bh80be5j7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24486",
  "fulltext_url": null,
  "id": "7wm6bh80be5j7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24486",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7223067417",
  "pdf_url": "https://arxiv.org/pdf/2610.24486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wm6bh80be5j7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Zero-trace index of matrices",
  "title_text": "Zero-trace index of matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7wm6bh80be5j7",
  "venue": "arXiv",
  "versions": []
}