{
  "id": "math/0310086",
  "version": "v1",
  "published": "2003-10-07T01:40:50.000Z",
  "updated": "2003-10-07T01:40:50.000Z",
  "title": "Differentiability of functions of matrices",
  "authors": [
    "Yury Grabovsky",
    "Omar Hijab",
    "Igor Rivin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA",
    "math.RT"
  ],
  "abstract": "Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times differentiable so is the extension (likewise for analyticity and the class k+alpha).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-07T01:40:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "15A42",
      "47A55"
    ],
    "keywords": [
      "differentiability",
      "extension preserves regularity",
      "diagonal matrices",
      "unique way",
      "symmetric matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10086G"
    }
  }
}