{
  "abstract": "We give a direct construction of the spectral projectors of a complex square matrix, based on explicit interpolation polynomials previously introduced. This yields a spectral resolution $A=\\sum_{i=1}^r(λ_iP_i+N_i)$ from which the Primary Decomposition Theorem, the Cayley--Hamilton theorem, criteria for diagonalizability, and the spectral theorem for normal matrices are proved by short formal arguments. A weaker form of the construction, extends to any perfect fields via a Galois invariance argument and produces the Jordan--Chevalley decomposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20218",
  "author_total": 2,
  "authors": [
    {
      "name": "Simon Bossoney"
    },
    {
      "name": "Marc Troyanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mh4hvm9p8xvd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20218",
  "fulltext_url": null,
  "id": "2mh4hvm9p8xvd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20218",
  "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",
      "math.OA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7170178514",
  "pdf_url": "https://arxiv.org/pdf/2607.20218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mh4hvm9p8xvd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2607.20218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Direct Polynomial Approach to Spectral Decomposition",
  "title_text": "A Direct Polynomial Approach to Spectral Decomposition",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2mh4hvm9p8xvd",
  "venue": "arXiv",
  "versions": []
}