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Overdetermined system — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Overdetermined_system
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T16:09:42.013Z
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Overdetermined system — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Overdetermined_system (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_fd4becd7bca2 (Metraipolis archive dc_fd4becd7bca2, sha256 a26c3d54f6397dfac0fa7f9855b33ca695d96622533177778c45b96e541b1713)

BibTeX

@misc{dcfd4becd7bca2,
  title = {Overdetermined system — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Overdetermined_system},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_fd4becd7bca2; sha256 a26c3d54f6397dfac0fa7f9855b33ca695d96622533177778c45b96e541b1713},
  year = {2026}
}

Archived text

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

In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others. The terminology can be described in terms of the concept of constraint counting. Each unknown can be seen as an available degree of freedom. Each equation introduced into the system can be viewed as a constraint that restricts one degree of freedom. Therefore, the critical case occurs when the number of equations and the number of free variables are equal. For every variable giving a degree of freedom, there exists a corresponding constraint. The overdetermined case occurs when the system has been overconstrained — that is, when the equations outnumber the unknowns. In contrast, the underdetermined case occurs when the system has been underconstrained — that is, when the number of equations is fewer than the number of unknowns. Such systems usually have an infinite number of solutions.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Overdetermined system» — https://en.wikipedia.org/wiki/Overdetermined_system
Wikidata Q331348 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q331348
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Overdetermined_system?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 1374903247, consultata il 2026-10-07T15:42:39.150Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: cb78acf93cc8bad68bec91d6affc396a10aeb45bad1d2f9b4a3996ae679db644