{
  "annotation_id": "b630cfc6-30a1-46bc-8185-5916ecb6a00b",
  "date_created": "2026-03-02T18:00:12.038000Z",
  "date_modified": "2026-03-02T18:00:12.038000Z",
  "file_hash": "497ac3f01176b815333aab626f3d62bfd8cf79618be79cbdafbfabc31b4cb90e",
  "private": false,
  "record": {
    "abstract": "The particular symmetry of the random-phase-approximation (RPA) matrix has\nbeen utilized in the past to reduce the RPA eigenvalue problem into a\nsymmetric-matrix problem of half the dimension. The condition of positive\ndefiniteness of at least one of the matrices A+-B has been imposed (where A and\nB are the submatrices of the RPA matrix) so that, e.g., its square root can be\nfound by Cholesky decomposition. In this work, alternative methods are pointed\nout to reduce the RPA problem to a real (not symmetric, in general) problem of\nhalf the dimension, with the condition of positive definiteness relaxed. One of\nthe methods relies on a generalized Cholesky decomposition, valid for\nnon-singular real symmetric matrices. The algorithm is described and a\ncorresponding routine in C is given.",
    "arxiv_id": "nucl-th/0702031",
    "authors": [
      "P. Papakonstantinou"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1209/0295-5075/78/12001",
    "journal_ref": "Europhys.Lett.78:12001,2007",
    "title": "Reduction of the RPA eigenvalue problem and a generalized Cholesky   decomposition for real-symmetric matrices",
    "url": "https://arxiv.org/abs/nucl-th/0702031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b6ab606c-a43d-4612-9bb1-c58ae98f4f48",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}