{
  "id": "1807.11749",
  "version": "v1",
  "published": "2018-07-31T10:45:29.000Z",
  "updated": "2018-07-31T10:45:29.000Z",
  "title": "Combinatorial proofs of some linear algebraic identities",
  "authors": [
    "Sajal Kumar Mukherjee",
    "Sudip Bera"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we give combinatorial proofs of some interesting linear algebraic identities. We also give an almost visual proof of Cramer's rule and a result of Chapman-Costas-santos regarding the determinant of sum of matrices. Also we find a new identity expressing permanent of sum of matrices. Besides, we give a graphical interpretation of Newton-Girard identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-31T10:45:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A05",
      "05C30",
      "05C38"
    ],
    "keywords": [
      "combinatorial proofs",
      "interesting linear algebraic identities",
      "identity expressing permanent",
      "visual proof",
      "newton-girard identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}