{
  "abstract": "We define a rank-two extension $\\mathcal{H}^{(2)}$ of the spherical $\\mathcal{H}$-transform, together with its associated transform $\\mathcal{R}^{(2)}$. For sums, both transforms are additive. The transform $\\mathcal{R}^{(2)}$ yields a $4\\times4$ formula for the average product of two hermitized resolvents, and hence for off-diagonal eigenvector overlaps, recovering the Ginibre, elliptic, and bi-invariant formulas. We also treat correlated pairs of matrices, and obtain overlaps between their eigenvectors or singular vectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22334",
  "author_total": 1,
  "authors": [
    {
      "name": "Pierre Bousseyroux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xpzhax979zgz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22334",
  "fulltext_url": null,
  "id": "5xpzhax979zgz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22334",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7214025007",
  "pdf_url": "https://arxiv.org/pdf/2609.22334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xpzhax979zgz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22334"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A rank-two spherical transform for eigenvector and singular-vector overlaps",
  "title_text": "A rank-two spherical transform for eigenvector and singular-vector overlaps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5xpzhax979zgz",
  "venue": "arXiv",
  "versions": []
}