{
  "id": "1206.5180",
  "version": "v2",
  "published": "2012-06-22T15:42:30.000Z",
  "updated": "2013-01-30T17:10:37.000Z",
  "title": "Invertibility of random matrices: unitary and orthogonal perturbations",
  "authors": [
    "Mark Rudelson",
    "Roman Vershynin"
  ],
  "comment": "46 pages. A more general result on orthogonal perturbations of complex matrices added. It rectified an inaccuracy in application to Single Ring Theorem for orthogonal matrices",
  "journal": "Journal of the AMS, 27 (2014), 293-338",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that a perturbation of any fixed square matrix D by a random unitary matrix is well invertible with high probability. A similar result holds for perturbations by random orthogonal matrices; the only notable exception is when D is close to orthogonal. As an application, these results completely eliminate a hard-to-check condition from the Single Ring Theorem by Guionnet, Krishnapur and Zeitouni.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-30T17:10:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "random matrices",
      "orthogonal perturbations",
      "invertibility",
      "random orthogonal matrices",
      "similar result holds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5180R"
    }
  }
}