{
  "id": "1805.11580",
  "version": "v1",
  "published": "2018-05-29T16:55:49.000Z",
  "updated": "2018-05-29T16:55:49.000Z",
  "title": "Algebraic Linearizations of Matrix Polynomials",
  "authors": [
    "Eunice Y. S. Chan",
    "Robert M. Corless",
    "Laureano Gonzalez-Vega",
    "J. Rafael Sendra",
    "Juana Sendra"
  ],
  "comment": "35 pages, 3 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We show how to construct linearizations of matrix polynomials $z\\mathbf{a}(z)\\mathbf{d}_0 + \\mathbf{c}_0$, $\\mathbf{a}(z)\\mathbf{b}(z)$, $\\mathbf{a}(z) + \\mathbf{b}(z)$ (when $\\mathrm{deg}\\left(\\mathbf{b}(z)\\right) < \\mathrm{deg}\\left(\\mathbf{a}(z)\\right)$), and $z\\mathbf{a}(z)\\mathbf{d}_0\\mathbf{b}(z) + \\mathbf{c_0}$ from linearizations of the component parts, $\\mathbf{a}(z)$ and $\\mathbf{b}(z)$. This allows the extension to matrix polynomials of a new companion matrix construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T16:55:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F99",
      "15A22"
    ],
    "keywords": [
      "matrix polynomials",
      "algebraic linearizations",
      "companion matrix construction",
      "component parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}