{
  "id": "1910.01966",
  "version": "v1",
  "published": "2019-10-04T14:22:56.000Z",
  "updated": "2019-10-04T14:22:56.000Z",
  "title": "Inertia indices and eigenvalue inequalities for Hermitian matrices",
  "authors": [
    "Sai-Nan Zheng",
    "Xi Chen",
    "Lily Li Liu",
    "Yi Wang"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a characterization of eigenvalue inequalities between two Hermitian matrices by means of inertia indices. As applications, we deal with some classical eigenvalue inequalities for Hermitian matrices, including the Cauchy interlacing theorem and the Weyl inequality, in a simple and unified approach. We also give a common generalization of eigenvalue inequalities for (Hermitian) normalized Laplacian matrices of simple (signed, weighted, directed) graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-04T14:22:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "05C50"
    ],
    "keywords": [
      "hermitian matrices",
      "inertia indices",
      "classical eigenvalue inequalities",
      "weyl inequality",
      "common generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}