{
  "id": "math/0504183",
  "version": "v1",
  "published": "2005-04-09T12:21:36.000Z",
  "updated": "2005-04-09T12:21:36.000Z",
  "title": "On sufficient conditions for the total positivity and for the multiple positivity of matrices",
  "authors": [
    "Olga M. Katkova",
    "Anna M. Vishnyakova"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RA"
  ],
  "abstract": "The following theorem is proved: Suppose $M = (a_{i,j})$ be a $k \\times k$ matrix with positive entries and $a_{i,j}a_{i+1,j+1} > 4\\cos ^2 \\frac{\\pi}{k+1} a_{i,j+1}a_{i+1,j} \\quad (1 \\leq i \\leq k-1, 1 \\leq j \\leq k-1).$ Then $\\det M > 0 .$ The constant $4\\cos ^2 \\frac{\\pi}{k+1}$ in this Theorem is sharp. A few other results concerning totally positive and multiply positive matrices are obtained. Keywords: Multiply positive matrix; Totally positive matrix; Strictly totally positive matrix; Toeplitz matrix; Hankel matrix; P\\'olya frequency sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-09T12:21:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A48",
      "15A57",
      "15A15"
    ],
    "keywords": [
      "multiple positivity",
      "sufficient conditions",
      "total positivity",
      "totally positive matrix",
      "polya frequency sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4183K"
    }
  }
}