{
  "id": "1906.10787",
  "version": "v1",
  "published": "2019-06-25T23:48:36.000Z",
  "updated": "2019-06-25T23:48:36.000Z",
  "title": "The p-norm of hypermatrices with symmetries",
  "authors": [
    "V. Nikiforov"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $p$-norm of $r$-matrices generalizes the $2$-norm of $2$-matrices. It is shown that if a nonnegative $r$-matrix is symmetric with respect to two indices $j$ and $k$, then the $p$-norm is attained for some set of vectors such that the $i$th and the $j$th vectors are identical. It follows that the $p$-spectral radius of a symmetric nonnegative $r$-matrix is equal to its $p$-norm for any $p\\geq2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-25T23:48:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C65",
      "15A18",
      "15A42",
      "15A60",
      "15A69"
    ],
    "keywords": [
      "symmetries",
      "hypermatrices",
      "matrices generalizes",
      "spectral radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}