{
  "id": "1109.0348",
  "version": "v3",
  "published": "2011-09-02T03:19:03.000Z",
  "updated": "2011-09-13T03:37:46.000Z",
  "title": "E-Determinants of Tensors",
  "authors": [
    "Shenglong Hu",
    "Zheng-Hai Huang",
    "Chen Ling",
    "Liqun Qi"
  ],
  "doi": "10.1016/j.jsc.2012.10.001",
  "categories": [
    "math.NA"
  ],
  "abstract": "We generalize the concept of the symmetric hyperdeterminants for symmetric tensors to the E-determinants for general tensors. We show that the E-determinant inherits many properties of the determinant of a matrix. These properties include: solvability of polynomial systems, the E-determinat of the composition of tensors, product formula for the E-determinant of a block tensor, Hadamard's inequality, Gersgrin's inequality and Minikowski's inequality. As a simple application, we show that if the leading coefficient tensor of a polynomial system is a triangular tensor with nonzero diagonal elements, then the system definitely has a solution. We investigate the characteristic polynomial of a tensor through the E-determinant. Explicit formulae for the coefficients of the characteristic polynomial are given when the dimension is two.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-13T03:37:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A15",
      "15A69",
      "15A72"
    ],
    "keywords": [
      "polynomial system",
      "characteristic polynomial",
      "nonzero diagonal elements",
      "gersgrins inequality",
      "block tensor"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0348H"
    }
  }
}