{
  "id": "1905.04807",
  "version": "v1",
  "published": "2019-05-12T23:27:19.000Z",
  "updated": "2019-05-12T23:27:19.000Z",
  "title": "Spectrum of some arrow-bordered circulant matrix",
  "authors": [
    "Wojciech Florek",
    "Adam Marlewski"
  ],
  "comment": "3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a circulant matrix $\\mathrm{circ}(c,a,0,0,...,0,a)$, $a\\ne 0$, of order~$n$, we ``border'' it from left and from above by constant column and row, respectively, and we set the left top entry to be $-nc$. This way we get a~particular title object, an example of what we call an \\textit{abc matrix\\/}, or an \\textit{arrow-bordered circulant (matrix)\\/}. We find its eigenpairs and we discuss its spectrum with stress on extreme eigenvalues and their bounds. At last we notice its relation to a~weighted wheel graph",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-12T23:27:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "05C50"
    ],
    "keywords": [
      "arrow-bordered circulant matrix",
      "extreme eigenvalues",
      "title object",
      "constant column",
      "eigenpairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}