{
  "id": "1004.4953",
  "version": "v2",
  "published": "2010-04-28T05:02:31.000Z",
  "updated": "2010-05-14T21:55:25.000Z",
  "title": "The Number of Eigenvalues of a Tensor",
  "authors": [
    "Dustin Cartwright",
    "Bernd Sturmfels"
  ],
  "comment": "12 pages, fixed several typos",
  "categories": [
    "math.NA",
    "math.AG"
  ],
  "abstract": "Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized eigenvalues of a symmetric tensor is always finite. We also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-14T21:55:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "15A69",
      "14M25"
    ],
    "keywords": [
      "eigenvectors",
      "numerical multilinear algebra",
      "generic tensor",
      "symmetric tensor",
      "characteristic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4953C"
    }
  }
}