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Orthogonalization — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Orthogonalization
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T16:09:38.958Z
SHA-256 of the archived text: 91dc22ff1680ac5736d89fbc9502465c9ba4d352cbe85ff95a9988cfa8ff3797
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Orthogonalization — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Orthogonalization (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_0e50bf4e9bc2 (Metraipolis archive dc_0e50bf4e9bc2, sha256 91dc22ff1680ac5736d89fbc9502465c9ba4d352cbe85ff95a9988cfa8ff3797)

BibTeX

@misc{dc0e50bf4e9bc2,
  title = {Orthogonalization — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Orthogonalization},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_0e50bf4e9bc2; sha256 91dc22ff1680ac5736d89fbc9502465c9ba4d352cbe85ff95a9988cfa8ff3797},
  year = {2026}
}

Archived text

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

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1, ... , uk} that generate the same subspace as the vectors v1, ... , vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span. In addition, if we want the resulting vectors to all be unit vectors, then we normalize each vector and the procedure is called orthonormalization. Orthogonalization is also possible with respect to any symmetric bilinear form (not necessarily an inner product, not necessarily over real numbers), but standard algorithms may encounter division by zero in this more general setting.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Orthogonalization» — https://en.wikipedia.org/wiki/Orthogonalization
Wikidata Q1702189 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1702189
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Orthogonalization?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 1299273509, consultata il 2026-10-07T15:42:39.136Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 3723456ed1d80745fcc3ec0fb61db74168c7078d4f75e68a4cd1515c9ef30736