{
  "annotation_id": "5888edd2-a1c8-48ce-989e-48712c16c4fe",
  "date_created": "2026-03-02T18:02:23.905000Z",
  "date_modified": "2026-03-02T18:02:23.905000Z",
  "file_hash": "8acfa5acad92a520168d269c458588170d3e98d86d44f3decc13c2fe4537e214",
  "private": false,
  "record": {
    "abstract": "We present a set of necessary conditions for the existence of a biorthonormal\nbasis composed of eigenvectors of non-Hermitian operators. As an illustration,\nwe examine these conditions in the case of normal operators. We also provide a\ngeneralization of the conditions which is applicable to non-diagonalizable\noperators by considering not only eigenvectors but also all root vectors.",
    "arxiv_id": "quant-ph/0603075",
    "authors": [
      "Toshiaki Tanaka"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "doi": "10.1088/0305-4470/39/24/012",
    "journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 7757-7761",
    "title": "On Existence of a Biorthonormal Basis Composed of Eigenvectors of   Non-Hermitian Operators",
    "url": "https://arxiv.org/abs/quant-ph/0603075"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "218a8866-b927-4850-bf08-a3c46f58b00f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}