{
  "id": "2206.02141",
  "version": "v1",
  "published": "2022-06-05T10:02:26.000Z",
  "updated": "2022-06-05T10:02:26.000Z",
  "title": "On low-dimensional partial isometries",
  "authors": [
    "Qixiao He",
    "Ilya M. Spitkovsky",
    "Ibrahim Suleiman"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "Two statements concerning $n$-by-$n$ partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for $n\\leq 4$ but fail starting with $n=5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-05T10:02:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "15B57",
      "15B99"
    ],
    "keywords": [
      "low-dimensional partial isometries",
      "circular disks",
      "statements hold",
      "numerical ranges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}