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Eigengap — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Eigengap
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T18:28:49.160Z
SHA-256 of the archived text: 46875a7c1107445d73fcac97a2d71647c7821bcfc8086e65fae5703e306be0c5
Stable URL of this page: https://metraipolis.com/documento/dc_460677221d4e

How to cite

Eigengap — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Eigengap (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_460677221d4e (Metraipolis archive dc_460677221d4e, sha256 46875a7c1107445d73fcac97a2d71647c7821bcfc8086e65fae5703e306be0c5)

BibTeX

@misc{dc460677221d4e,
  title = {Eigengap — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Eigengap},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_460677221d4e; sha256 46875a7c1107445d73fcac97a2d71647c7821bcfc8086e65fae5703e306be0c5},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Eigengap. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In linear algebra, the eigengap of a linear operator is the difference between two successive eigenvalues, where eigenvalues are sorted in ascending order. The Davis–Kahan theorem, named after Chandler Davis and William Kahan, uses the eigengap to show how eigenspaces of an operator change under perturbation. Essentially, a larger eigengap indicates that the corresponding eigenvectors are more robust and less sensitive to small changes or noise in the data. In spectral clustering, the eigengap is often referred to as the spectral gap; although the spectral gap may often be defined in a broader sense than that of the eigengap. In this context, a significant jump or gap between successive eigenvalues often suggests a natural division in the underlying data structure, helping to determine the ideal number of clusters.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «linear algebra»).
Fonte: Wikipedia in inglese, voce «Eigengap» — https://en.wikipedia.org/wiki/Eigengap
Wikidata Q5348905: «difference between successive eigenvalues» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5348905
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Eigengap?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1347301284, consultata il 2026-10-07T17:57:22.127Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 16eeee9f77d0da806de2b36eb69c21cf887ee0dc25275fb5d09acf493bd6c19d