{
  "abstract": "In this paper, we study the elliptical shape of the numerical range of tridiagonal matrices of orders $3,4$ and $5$ with zero entries on the main diagonal, a positive constant value $a$ along the super-diagonal, and sub-diagonal entries are \\begin{align*} \\begin{cases} r, sr^2, r^3, sr^4,\\ldots, r^{n-1} & \\mbox{ if $n$ is even, and } r, sr^2, r^3, sr^4,\\ldots, sr^{n-1} & \\mbox{ if $n$ is odd}, \\end{cases} \\end{align*} where $n$ denotes the order of the matrix, $s>0$ and $r$ is a real number. We further investigate the flat portions on the boundary of the numerical range of these $n\\times n$ matrices in the special case $r=-1$. Some results given in \\cite{chien2011numerical} are obtained as a particular case of our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31231",
  "author_total": 4,
  "authors": [
    {
      "name": "Arobinda Ghosh"
    },
    {
      "name": "Riddhick Birbonshi"
    },
    {
      "name": "Sarita Ojha"
    },
    {
      "name": "Kallol Paul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mjgqt8zsfzs4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31231",
  "fulltext_url": null,
  "id": "0mjgqt8zsfzs4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31231",
  "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.FA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7214666428",
  "pdf_url": "https://arxiv.org/pdf/2609.31231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mjgqt8zsfzs4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the shape of the numerical range of some tridiagonal matrices",
  "title_text": "On the shape of the numerical range of some tridiagonal matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/0mjgqt8zsfzs4",
  "venue": "arXiv",
  "versions": []
}