{
  "id": "1612.05058",
  "version": "v1",
  "published": "2016-12-15T13:35:50.000Z",
  "updated": "2016-12-15T13:35:50.000Z",
  "title": "New pairs of matrices with convex generalized numerical ranges",
  "authors": [
    "Wai-Shun Cheung"
  ],
  "doi": "10.1080/03081087.2016.1255173",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we are going to search for $n\\times n$ matrices $A$ and $B$ such that their generalized numerical range $$W_A(B)=\\{tr(AU^*BU) \\ :\\ U^*U=UU^*=I\\}$$ is convex. More specifically, we consider $A=\\hat{A}\\oplus I_k$ and $B=\\hat{B}\\oplus I_k$ where $\\hat{A}$ and $\\hat{B}$ are $2\\times 2$. If $W_A(B)=W_{\\hat{A}}(\\hat{B})$ then it is a convex set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-15T13:35:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60"
    ],
    "keywords": [
      "convex generalized numerical ranges",
      "convex set"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}