# Rank

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Position in a hierarchy

For other uses, see [Rank (disambiguation)](/source/Rank_(disambiguation)).

A **rank** is a position in a [hierarchy](/source/Hierarchy). It can be formally recognized—for example, [cardinal](/source/Cardinal_(Catholic_Church)), [chief executive officer](/source/Chief_executive_officer), [general](/source/General_officer), [professor](/source/Professor)—or unofficial.

## People

### Formal ranks

- [Academic rank](/source/Academic_rank)

- [Corporate title](/source/Corporate_title)

- [Diplomatic rank](/source/Diplomatic_rank)

- [Hierarchy of the Catholic Church](/source/Hierarchy_of_the_Catholic_Church)

- [Imperial, royal and noble ranks](/source/Imperial%2C_royal_and_noble_ranks)

- [Military rank](/source/Military_rank)

- [Police rank](/source/Police_rank)

### Unofficial ranks

- [Social class](/source/Social_class)

- [Social position](/source/Social_position)

- [Social status](/source/Social_status)

### Either

- [Seniority](/source/Seniority)

## Mathematics

- [Rank (differential topology)](/source/Rank_(differential_topology))

- [Rank (graph theory)](/source/Rank_(graph_theory))

- [Rank (linear algebra)](/source/Rank_(linear_algebra)), the dimension of the vector space generated (or spanned) by a matrix's columns

- [Rank (set theory)](/source/Rank_(set_theory))

- [Rank (type theory)](/source/Rank_(type_theory))

- [Rank of an abelian group](/source/Rank_of_an_abelian_group), the cardinality of a maximal linearly independent subset

- [Rank of an elliptic curve](/source/Rank_of_an_elliptic_curve)

- Rank of a [free module](/source/Free_module)

- Rank of a [generalized eigenvector](/source/Generalized_eigenvector)

- Rank of a [greedoid](/source/Greedoid), the maximal size of a feasible set

- [Rank of a group](/source/Rank_of_a_group), the smallest cardinality of a generating set for the group

- Rank of a Lie group – see [Cartan subgroup](/source/Cartan_subgroup)

- Rank of a [matroid](/source/Matroid), the maximal size of an independent set

- [Rank of a partition](/source/Rank_of_a_partition), at least two definitions in number theory

- [Rank of a tensor](/source/Rank_of_a_tensor)

- Rank of a [vector bundle](/source/Vector_bundle)

- [Rank statistics](/source/Rank_statistics)

## Other

- [Taxonomic rank](/source/Taxonomic_rank), in biology

- [Rank (J programming language)](/source/Rank_(J_programming_language))

## See also

Look up ***[rank](https://en.wiktionary.org/wiki/rank)*** in Wiktionary, the free dictionary.

[Wikisource](/source/Wikisource) has the text of the [1911 *Encyclopædia Britannica*](/source/Encyclop%C3%A6dia_Britannica_Eleventh_Edition) article "[Rank](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Rank)".

Wikiquote has quotations related to ***[Rank](https://en.wikiquote.org/wiki/Special:Search/Rank)***.

- [All pages with titles containing *rank*](https://en.wikipedia.org/wiki/Special:Search/intitle:%22rank%22)

- [Ranking](/source/Ranking)

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Adapted from the Wikipedia article [Rank](https://en.wikipedia.org/wiki/Rank) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Rank?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.