{
  "id": "0807.3580",
  "version": "v2",
  "published": "2008-07-23T00:08:50.000Z",
  "updated": "2009-12-17T04:34:14.000Z",
  "title": "Zero patterns and unitary similarity",
  "authors": [
    "Jinpeng An",
    "Dragomir Z. Djokovic"
  ],
  "comment": "39 pages",
  "journal": "Journal of Algebra 324 (2010) 51-80",
  "categories": [
    "math.RT"
  ],
  "abstract": "A subspace of the space, L(n), of traceless complex $n\\times n$ matrices can be specified by requiring that the entries at some positions $(i,j)$ be zero. The set, $I$, of these positions is a (zero) pattern and the corresponding subspace of L(n) is denoted by $L_I(n)$. A pattern $I$ is universal if every matrix in L(n) is unitarily similar to some matrix in $L_I(n)$. The problem of describing the universal patterns is raised, solved in full for $n\\le3$, and partial results obtained for $n=4$. Two infinite families of universal patterns are constructed. They give two analogues of Schur's triangularization theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-17T04:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "14L35"
    ],
    "keywords": [
      "unitary similarity",
      "zero patterns",
      "universal patterns",
      "schurs triangularization theorem",
      "partial results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3580A"
    }
  }
}