{
  "id": "1011.0040",
  "version": "v1",
  "published": "2010-10-30T02:55:39.000Z",
  "updated": "2010-10-30T02:55:39.000Z",
  "title": "Criterion of unitary similarity for upper triangular matrices in general position",
  "authors": [
    "Douglas Farenick",
    "Vyacheslav Futorny",
    "Tatiana G. Gerasimova",
    "Vladimir V. Sergeichuk",
    "Nadya Shvai"
  ],
  "comment": "16 pages",
  "journal": "Linear Algebra Appl. 435 (2011) 1356-1369",
  "doi": "10.1016/j.laa.2011.03.021",
  "categories": [
    "math.RT"
  ],
  "abstract": "Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to direct sums of matrices of smaller sizes, or (ii) are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if ||h(A_k)||=||h(B_k)|| for all complex polynomials h(x) and k=1, 2, . . , n, where A_k and B_k are the principal k-by-k submatrices of A and B, and ||M|| is the Frobenius norm of M.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-30T02:55:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "15A60"
    ],
    "keywords": [
      "upper triangular matrices",
      "general position",
      "unitary similarity",
      "upper triangular n-by-n matrices",
      "unitarily similar"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0040F"
    }
  }
}