{
  "id": "math/0609572",
  "version": "v2",
  "published": "2006-09-20T19:13:09.000Z",
  "updated": "2006-09-21T16:49:07.000Z",
  "title": "Graphs and Hermitian matrices: exact interlacing",
  "authors": [
    "Bela Bollobas",
    "Vladimir Nikiforov"
  ],
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-21T16:49:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "hermitian matrices",
      "exact interlacing",
      "largest singular value",
      "lower bound",
      "extreme eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9572B"
    }
  }
}