{
  "id": "1811.03227",
  "version": "v1",
  "published": "2018-11-08T02:34:51.000Z",
  "updated": "2018-11-08T02:34:51.000Z",
  "title": "On Wielandt-Mirsky's conjecture for matrix polynomials",
  "authors": [
    "Công-Trình Lê"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In matrix analysis, the Wielandt-Mirsky's conjecture states that $$ dist(\\sigma(A), \\sigma(B)) \\leq \\|A-B\\|, $$ for any normal matrices $ A, B \\in \\mathbb C^{n\\times n}$ and any operator norm $\\|\\cdot \\|$ on $C^{n\\times n}$. Here $dist(\\sigma(A), \\sigma(B))$ denotes the optimal matching distance between the spectra of the matrices $A$ and $ B$. It was proved by A.J. Holbrook (1992) that this conjecture is \\textit{false} in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt's inequality). The main aim of this paper is to study the Hoffman-Wielandt's inequality and some weaker versions of the Wielandt-Mirsky's conjecture for matrix polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T02:34:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "15A42",
      "15A60",
      "65F15"
    ],
    "keywords": [
      "matrix polynomials",
      "hoffman-wielandts inequality",
      "wielandt-mirskys conjecture states",
      "normal matrices",
      "operator norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}