{
  "id": "2205.15742",
  "version": "v1",
  "published": "2022-05-29T16:36:36.000Z",
  "updated": "2022-05-29T16:36:36.000Z",
  "title": "Bidiagonal decompositions and total positivity of some special matrices",
  "authors": [
    "Priyanka Grover",
    "Veer Singh Panwar"
  ],
  "comment": "This article contains 15 pages",
  "categories": [
    "math.RA"
  ],
  "abstract": "The matrix $S = [1+x_i y_j]_{i,j=1}^{n}, 0<x_1<\\cdots<x_n,\\, 0<y_1<\\cdots<y_n$, has gained importance lately due to its role in powers preserving total nonnegativity. We give an explicit decomposition of $S$ in terms of elementary bidiagonal matrices, which is analogous to the Neville decomposition. We give a bidiagonal decomposition of $S^{\\circ m}=[(1+x_iy_j)^m]$ for positive integers $1\\leq m \\leq n-1$. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-29T16:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B05",
      "15A23",
      "15B48"
    ],
    "keywords": [
      "bidiagonal decomposition",
      "total positivity",
      "special matrices",
      "powers preserving total nonnegativity",
      "elementary bidiagonal matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}