{
  "id": "1605.04416",
  "version": "v1",
  "published": "2016-05-14T13:23:08.000Z",
  "updated": "2016-05-14T13:23:08.000Z",
  "title": "On the similarity of AB and BA for normal and other matrices",
  "authors": [
    "Stephan Ramon Garcia",
    "David Sherman",
    "Gary Weiss"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "It is well-known that AB and BA are similar when A and B are complex square Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if A is Hermitian and B is normal. Perhaps surprisingly, similarity does hold when A is positive semidefinite and B is normal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-14T13:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A03",
      "15A18"
    ],
    "keywords": [
      "similarity",
      "complex square hermitian matrices",
      "well-known",
      "positive semidefinite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}