{
  "id": "1510.04419",
  "version": "v1",
  "published": "2015-10-15T07:02:39.000Z",
  "updated": "2015-10-15T07:02:39.000Z",
  "title": "Characteristic polynomials of typical matrices are ill-conditioned",
  "authors": [
    "Peter Buergisser",
    "Felipe Cucker",
    "Elisa Rocha Cardozo"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is $\\Omega(n)$. This gives a rigorous justification of the common wisdom in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-15T07:02:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic polynomial",
      "typical matrices",
      "complex standard gaussian matrix",
      "condition number",
      "common wisdom"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151004419B"
    }
  }
}