{
  "id": "1307.7519",
  "version": "v2",
  "published": "2013-07-29T09:53:42.000Z",
  "updated": "2014-05-19T14:17:03.000Z",
  "title": "On the maximum angle between copositive matrices",
  "authors": [
    "Felix Goldberg",
    "Naomi Shaked-Monderer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle $\\theta_{\\max}(\\mathcal{C}_{n})$ between two copositive matrices of order $n$. They have proved that $\\theta_{\\max}(\\mathcal{C}_{2})=\\frac{3}{4}\\pi$ and conjectured that $\\theta_{\\max}(\\mathcal{C}_{n})$ is equal to $\\frac{3}{4}\\pi$ for all $n \\geq 2$. In this note we disprove their conjecture by showing that $\\lim_{n \\rightarrow \\infty}{\\theta_{\\max}(\\mathcal{C}_{n})}=\\pi$. Our proof uses a construction from algebraic graph theory. We also consider the related problem of finding the maximal angle between a nonnegative matrix and a positive semidefinite matrix of the same order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-19T14:17:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A48",
      "52A40",
      "05E30"
    ],
    "keywords": [
      "copositive matrices",
      "maximum angle",
      "algebraic graph theory",
      "maximal angle",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7519G"
    }
  }
}