{
  "id": "1011.6325",
  "version": "v1",
  "published": "2010-11-20T17:38:33.000Z",
  "updated": "2010-11-20T17:38:33.000Z",
  "title": "A trace inequality for positive definite matrices",
  "authors": [
    "E. V. Belmega",
    "S. Lasaulce",
    "M. Debbah"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note we prove that Tr (MN+ PQ)>= 0 when the following two conditions are met: (i) the matrices M, N, P, Q are structured as follows: M = A -B, N = inv(B)-inv(A), P = C-D, Q =inv (B+D)-inv(A+C), where inv(X) denotes the inverse matrix of X (ii) A, B are positive definite matrices and C, D are positive semidefinite matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-20T17:38:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive definite matrices",
      "trace inequality",
      "positive semidefinite matrices",
      "inverse matrix",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.6325B"
    }
  }
}