{
  "id": "0909.4262",
  "version": "v5",
  "published": "2009-09-23T18:09:26.000Z",
  "updated": "2012-10-09T09:32:18.000Z",
  "title": "Ranks of tensors and a generalization of secant varieties",
  "authors": [
    "Jarosław Buczyński",
    "J. M. Landsberg"
  ],
  "comment": "22 pages; final published version; Linear Algebra and its Applications 2012",
  "journal": "Linear Algebra and Its Applications 438 (2013), pp. 668-689 (Special Issue \"Tensors and Multilinear Algebra\")",
  "doi": "10.1016/j.laa.2012.05.001",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \\otimes C^b \\otimes C^b. We review the literature from a geometric perspective.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-10-09T09:32:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Q20",
      "15A69",
      "15A21"
    ],
    "keywords": [
      "secant varieties",
      "generalization",
      "upper bound",
      "partially symmetric tensors",
      "subspace rank"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4262B"
    }
  }
}