{
  "id": "2408.12660",
  "version": "v1",
  "published": "2024-08-22T18:07:48.000Z",
  "updated": "2024-08-22T18:07:48.000Z",
  "title": "Stability of Matrix Recurrence Relations",
  "authors": [
    "Glenn Bruda",
    "Bruce Fang",
    "Pico Gilman",
    "Raul Marquez",
    "Steven J. Miller",
    "Beni Prapashtica",
    "Daeyoung Son",
    "Saad Waheed",
    "Janine Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by the rich properties and various applications of recurrence relations, we consider the extension of traditional recurrence relations to matrices, where we use matrix multiplication and the Kronecker product to construct matrix sequences. We provide a sharp condition, which when satisfied, guarantees that any fixed-depth matrix recurrence relation defined over a product (with respect to matrix multiplication) will converge to the zero matrix. We also show that the same statement applies to matrix recurrence relations defined over a Kronecker product. Lastly, we show that the dual of this condition, which remains sharp, guarantees the divergence of matrix recurrence relations defined over a consecutive Kronecker product. These results completely determine the stability of nontrivial fixed-depth complex-valued recurrence relations defined over a consecutive product.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-22T18:07:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B39",
      "15A24"
    ],
    "keywords": [
      "kronecker product",
      "nontrivial fixed-depth complex-valued recurrence relations",
      "matrix multiplication",
      "fixed-depth matrix recurrence relation",
      "construct matrix sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}