{
  "id": "2106.12019",
  "version": "v1",
  "published": "2021-06-22T18:56:31.000Z",
  "updated": "2021-06-22T18:56:31.000Z",
  "title": "Length-Preserving Directions and Some Diophantine Equations",
  "authors": [
    "Juan Tolosa"
  ],
  "comment": "5 figures",
  "journal": "American Mathematical Monthly 128:2, 125-139, February 2021",
  "doi": "10.1080/00029890",
  "categories": [
    "math.NT",
    "math.SP"
  ],
  "abstract": "We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail, and also discuss the extension to the three-dimensional case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-22T18:56:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "11D09",
      "15A06"
    ],
    "keywords": [
      "diophantine equations",
      "length-preserving directions",
      "linear map",
      "study directions",
      "two-dimensional case"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}