{
  "annotation_id": "2a4a7a16-6b06-4dcc-afa7-924a9b93662d",
  "date_created": "2026-03-02T18:02:27.457000Z",
  "date_modified": "2026-03-02T18:02:27.457000Z",
  "file_hash": "facdaf382e09edde70a4d5688f217f4e0cfcd432321482537fbe1d446c9d5f1a",
  "private": false,
  "record": {
    "abstract": "How to calculate the exponential of matrices in an explicit manner is one of\nfundamental problems in almost all subjects in Science.\n  Especially in Mathematical Physics or Quantum Optics many problems are\nreduced to this calculation by making use of some approximations whether they\nare appropriate or not. However, it is in general not easy.\n  In this paper we give a very useful formula which is both elementary and\ngetting on with computer.",
    "arxiv_id": "quant-ph/0604115",
    "authors": [
      "Kazuyuki Fujii",
      "Hiroshi Oike"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "journal_ref": "Far East Journal of Mathematical Education, 9(2012) 39-55",
    "title": "How to Calculate the Exponential of Matrices",
    "url": "https://arxiv.org/abs/quant-ph/0604115"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d31721fc-019d-4292-873c-ef18eada6ccc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}