{
  "id": "1202.2025",
  "version": "v2",
  "published": "2012-02-09T16:03:48.000Z",
  "updated": "2012-08-06T09:50:38.000Z",
  "title": "Almost Hadamard matrices: general theory and examples",
  "authors": [
    "Teodor Banica",
    "Ion Nechita",
    "Karol Zyczkowski"
  ],
  "comment": "24 pages",
  "journal": "Open Syst. Inf. Dyn. 19 (2012), 1-26",
  "categories": [
    "math.CO",
    "quant-ph"
  ],
  "abstract": "We develop a general theory of \"almost Hadamard matrices\". These are by definition the matrices $H\\in M_N(\\mathbb R)$ having the property that $U=H/\\sqrt{N}$ is orthogonal, and is a local maximum of the 1-norm on O(N). Our study includes a detailed discussion of the circulant case ($H_{ij}=\\gamma_{j-i}$) and of the two-entry case ($H_{ij}\\in{x,y}$), with the construction of several families of examples, and some 1-norm computations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-06T09:50:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general theory",
      "hadamard matrices",
      "local maximum",
      "circulant case",
      "two-entry case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2025B"
    }
  }
}