{
  "id": "1206.0370",
  "version": "v3",
  "published": "2012-06-02T12:14:14.000Z",
  "updated": "2016-01-21T06:44:06.000Z",
  "title": "Arithmetic, geometric, and harmonic means for accretive-dissipative matrices",
  "authors": [
    "Minghua Lin"
  ],
  "comment": "The paper is not mature",
  "categories": [
    "math.FA"
  ],
  "abstract": "The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM inequality is established for two accretive-dissipative matrices in the sense of this extended Loewner order. We also compare the harmonic mean and parallel sum of two accretive-dissipative matrices, revealing an interesting relation between them. A number of examples are included.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-14T14:14:02.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-01-21T06:44:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "accretive-dissipative matrices",
      "harmonic mean",
      "arithmetic",
      "general complex matrices",
      "parallel sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0370L"
    }
  }
}