{
  "id": "2209.14840",
  "version": "v1",
  "published": "2022-09-29T14:56:59.000Z",
  "updated": "2022-09-29T14:56:59.000Z",
  "title": "Necessary and sufficient conditions for a subclass of $P$-tensor",
  "authors": [
    "R. Deb",
    "A. K. Das"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this article, we introduce the class $B$-Nekrasov tensor in the context of tensor complementarity problem. We study some tensor theoretic properties. We show that the class of B-Nekrasov tensor contains the class of Nekrasov $Z$-tensor with positive diagonal entries. We present a necessary and sufficient condition for a $B$-Nekrasov tensor. We show that the class of $P$-tensor contains the class of $B$-Nekrasov tensor. Keywords: Tensor complementarity problem, $P$-tensors, Nekrasov tensors, Nekrasov $Z$-tensor, $B$-Nekrasov tensors, Nonsingular $H$-tensor, Diagonally dominant tensor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-29T14:56:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "tensor complementarity problem",
      "tensor theoretic properties",
      "b-nekrasov tensor contains",
      "positive diagonal entries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}