{
  "id": "0908.2107",
  "version": "v4",
  "published": "2009-08-14T17:26:02.000Z",
  "updated": "2011-08-09T19:27:40.000Z",
  "title": "Unitary equivalence of a matrix to its transpose",
  "authors": [
    "Stephan Ramon Garcia",
    "James E. Tener"
  ],
  "comment": "22 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Motivated by a problem of Halmos, we obtain a canonical decomposition for complex matrices which are unitarily equivalent to their transpose (UET). Surprisingly, the naive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix (i.e., $T = T^t$) holds for matrices 7x7 and smaller, but fails for matrices 8x8 and larger.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-08-09T19:27:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A57",
      "47A30"
    ],
    "keywords": [
      "unitary equivalence",
      "complex symmetric matrix",
      "unitarily equivalent",
      "complex matrices",
      "matrices 8x8"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2107G"
    }
  }
}