{
  "id": "1712.08729",
  "version": "v1",
  "published": "2017-12-23T07:58:43.000Z",
  "updated": "2017-12-23T07:58:43.000Z",
  "title": "Reduction of a pair of skew-symmetric matrices to its canonical form under congruence",
  "authors": [
    "V. A. Bovdi",
    "T. G. Gerasimova",
    "M. A. Salim",
    "V. V. Sergeichuk"
  ],
  "comment": "16 pages",
  "journal": "Linear Algebra Appl. 543 (2018) 17-30",
  "doi": "10.1016/j.laa.2017.12.013",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(A,B)$ be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum \\[ (\\underline{\\underline A},\\underline{\\underline B})\\oplus (A_1,B_1)\\oplus\\dots\\oplus(A_t,B_t) \\] that is congruent to $(A,B)$, in which $(\\underline{\\underline A},\\underline{\\underline B})$ is a pair of nonsingular matrices and $(A_1,B_1),$ $\\dots,$ $(A_t,B_t)$ are singular indecomposable canonical pairs of skew-symmetric matrices under congruence. We give an algorithm that constructs a regularization decomposition. We also give a constructive proof of the known canonical form of $(A,B)$ under congruence over an algebraically closed field of characteristic not 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-23T07:58:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "15A22",
      "15A63",
      "51A50"
    ],
    "keywords": [
      "skew-symmetric matrices",
      "canonical form",
      "congruence",
      "regularization decomposition",
      "characteristic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}