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Flag (linear algebra) — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Flag_(linear_algebra)
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T11:22:32.607Z
SHA-256 of the archived text: d657d62be001dd18d15662b2dcf8f6b7d5f1d906c8d9d68606e2b7ad7efb5deb
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Flag (linear algebra) — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Flag_(linear_algebra) (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_fd4ebee26171 (Metraipolis archive dc_fd4ebee26171, sha256 d657d62be001dd18d15662b2dcf8f6b7d5f1d906c8d9d68606e2b7ad7efb5deb)

BibTeX

@misc{dcfd4ebee26171,
  title = {Flag (linear algebra) — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Flag_(linear_algebra)},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_fd4ebee26171; sha256 d657d62be001dd18d15662b2dcf8f6b7d5f1d906c8d9d68606e2b7ad7efb5deb},
  year = {2026}
}

Archived text

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

In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): { 0 } = V 0 ⊂ V 1 ⊂ V 2 ⊂ ⋯ ⊂ V k = V . {\displaystyle \{0\}=V_{0}\subset V_{1}\subset V_{2}\subset \cdots \subset V_{k}=V.} The term flag is motivated by a particular example resembling a flag: the zero point, a line, and a plane correspond to a nail, a staff, and a sheet of fabric. If we write that dimVi = di then we have 0 = d 0 < d 1 < d 2 < ⋯ < d k = n , {\displaystyle 0=d_{0}<d_{1}<d_{2}<\cdots <d_{k}=n,} where n is the dimension of V (assumed to be finite). Hence, we must have k ≤ n. A flag is called a complete flag if di = i for all i, otherwise it is called a partial flag. A partial flag can be obtained from a complete flag by deleting some of the subspaces. Conversely, any partial flag can be completed (in many different ways) by inserting suitable subspaces. The signature of the flag is the sequence (d1, ..., dk).

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Flag (linear algebra)» — https://en.wikipedia.org/wiki/Flag_(linear_algebra)
Wikidata Q1392130 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1392130
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Flag_(linear_algebra)?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 1364190137, consultata il 2026-10-07T11:15:31.879Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d97be138dc34e3929e4303223dec52fa6dc9b3722e087530fc67b7460feda6a2