{
  "id": "math/0611947",
  "version": "v1",
  "published": "2006-11-30T12:34:46.000Z",
  "updated": "2006-11-30T12:34:46.000Z",
  "title": "A geometric estimate on the norm of product of functionals",
  "authors": [
    "Mate Matolcsi"
  ],
  "comment": "7 pages",
  "journal": "Linear Algebra Appl. 405 (2005), 304--310",
  "categories": [
    "math.CA"
  ],
  "abstract": "The open problem of determining the exact value of the $n$-th linear polarization constant $c_n$ of $\\R^n$ has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of $\\sup_{\\|{\\bf{y}}\\|=1}| {\\bf{x}}_1,{\\bf{y}} ... {\\bf{x}}_n,{\\bf{y}} |$, where ${\\bf{x}}_1, ... ,{\\bf{x}}_n$ are unit vectors in $\\R^n$. The new estimate is given in terms of the eigenvalues of the Gram matrix $[ {\\bf{x}}_i,{\\bf{x}}_j ]$ and improves upon earlier estimates of this kind. However, the intriguing conjecture $c_n=n^{n/2}$ remains open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-30T12:34:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G25",
      "52A40",
      "46B07"
    ],
    "keywords": [
      "geometric estimate",
      "functionals",
      "th linear polarization constant",
      "gram matrix",
      "exact value"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11947M"
    }
  }
}