{
  "abstract": "We construct coordinates on orthogonal conjugacy classes of traceless real symmetric matrices with arbitrary spectrum (the isospectral manifold) that diagonalize the non-periodic Toda vector field. The coordinates, defined on a neighborhood of any diagonal matrix decouple the Toda vector field into a sum of multiples of the Euler vector field in $\\mathbb{R}$. The domain of each set of coordinates is dense and their union covers the isospectral manifold. The construction relies on a new matrix factorization which is of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07263",
  "author_total": 2,
  "authors": [
    {
      "name": "David Martínez Torres"
    },
    {
      "name": "Carlos Tomei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w5neqj1q9b9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07263",
  "fulltext_url": null,
  "id": "3w5neqj1q9b9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07263",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7202142122",
  "pdf_url": "https://arxiv.org/pdf/2608.07263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w5neqj1q9b9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.07263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices",
  "title_text": "Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/3w5neqj1q9b9g",
  "venue": "arXiv",
  "versions": []
}