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Krylov subspace — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Krylov_subspace
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-31T14:36:08.811Z
SHA-256 of the archived text: 6eecff2e50d0bd3ee0f639aacbb1cc0b84317e0aba567f60d554523dbf3276af
Stable URL of this page: https://metraipolis.com/documento/dc_cc366cc518ff

How to cite

Krylov subspace — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Krylov_subspace (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_cc366cc518ff (Metraipolis archive dc_cc366cc518ff, sha256 6eecff2e50d0bd3ee0f639aacbb1cc0b84317e0aba567f60d554523dbf3276af)

BibTeX

@misc{dccc366cc518ff,
  title = {Krylov subspace — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Krylov_subspace},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_cc366cc518ff; sha256 6eecff2e50d0bd3ee0f639aacbb1cc0b84317e0aba567f60d554523dbf3276af},
  year = {2026}
}

Archived text

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

In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A (starting from A 0 = I {\displaystyle A^{0}=I} ), that is, K r ( A , b ) = span { b , A b , A 2 b , … , A r − 1 b } . {\displaystyle {\mathcal {K}}_{r}(A,b)=\operatorname {span} \,\{b,Ab,A^{2}b,\ldots ,A^{r-1}b\}.}

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «linear algebra»).
Fonte: Wikipedia in inglese, voce «Krylov subspace» — https://en.wikipedia.org/wiki/Krylov_subspace
Wikidata Q1757151 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1757151
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Krylov_subspace?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 1375565401, consultata il 2026-10-31T14:24:58.207Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 99f95f0a1f1720ecb639b8a98818d296822b7660f8b088e9130d32e1c205c7e2