{
  "id": "1311.0764",
  "version": "v1",
  "published": "2013-11-04T16:44:27.000Z",
  "updated": "2013-11-04T16:44:27.000Z",
  "title": "Submatrices of Hadamard matrices: complementation results",
  "authors": [
    "Teo Banica",
    "Ion Nechita",
    "Jean-Marc Schlenker"
  ],
  "journal": "Electron. J. Linear Algebra 27 (2014), 197-212",
  "categories": [
    "math.CO",
    "math.FA"
  ],
  "abstract": "Two submatrices $A,D$ of a Hadamard matrix $H$ are called complementary if, up to a permutation of rows and columns, $H=[^A_C{\\ }^B_D]$. We find here an explicit formula for the polar decomposition of $D$. As an application, we show that under suitable smallness assumptions on the size of $A$, the complementary matrix $D$ is an almost Hadamard sign pattern, i.e. its rescaled polar part is an almost Hadamard matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-04T16:44:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B34"
    ],
    "keywords": [
      "hadamard matrices",
      "complementation results",
      "submatrices",
      "hadamard matrix",
      "rescaled polar part"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0764B"
    }
  }
}