{
  "id": "quant-ph/0305156",
  "version": "v1",
  "published": "2003-05-26T08:10:05.000Z",
  "updated": "2003-05-26T08:10:05.000Z",
  "title": "Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds",
  "authors": [
    "Petre Dita"
  ],
  "comment": "21 pages",
  "journal": "J.Phys. A38 (2005) 2657-2668",
  "doi": "10.1088/0305-4470/38/12/008",
  "categories": [
    "quant-ph",
    "hep-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-26T08:10:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.30.Tb",
      "02.10.Sp"
    ],
    "keywords": [
      "hermitian operators",
      "grassmann manifolds",
      "finite-level systems",
      "novel parameterization",
      "isometries"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 619879
    }
  }
}