{
  "id": "math/0703307",
  "version": "v1",
  "published": "2007-03-11T17:17:08.000Z",
  "updated": "2007-03-11T17:17:08.000Z",
  "title": "The condition number of a randomly perturbed matrix",
  "authors": [
    "Terence Tao",
    "Van Vu"
  ],
  "comment": "8 pages, no figures, to appear, STOC '07",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $M$ be an arbitrary $n$ by $n$ matrix. We study the condition number a random perturbation $M+N_n$ of $M$, where $N_n$ is a random matrix. It is shown that, under very general conditions on $M$ and $M_n$, the condition number of $M+N_n$ is polynomial in $n$ with very high probability. The main novelty here is that we allow $N_n$ to have discrete distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-11T17:17:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "condition number",
      "randomly perturbed matrix",
      "random perturbation",
      "discrete distribution",
      "random matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3307T"
    }
  }
}