View source for Rank

{{Short description|A position in a hierarchy}}
{{other uses}}
A '''rank''' is a position in a [[hierarchy]]. It can be formally recognized&mdash;for example, [[Cardinal (Catholic Church)|cardinal]], [[chief executive officer]], [[General officer|general]], [[professor]]&mdash;or unofficial.
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==People==
===Formal ranks===
* [[Academic rank]]
* [[Corporate title]]
* [[Diplomatic rank]]
* [[Hierarchy of the Catholic Church]]
* [[Imperial, royal and noble ranks]]
* [[Military rank]]
* [[Police rank]]

===Unofficial ranks===
* [[Social class]]
* [[Social position]]
* [[Social status]]

===Either===
* [[Seniority]]

==Mathematics==
* [[Rank (differential topology)]]
* [[Rank (graph theory)]]
* [[Rank (linear algebra)]], the dimension of the vector space generated (or spanned) by a matrix's columns
* [[Rank (set theory)]]
* [[Rank (type theory)]]
* [[Rank of an abelian group]], the cardinality of a maximal linearly independent subset
* Rank of a [[free module]]
* Rank of a [[generalized eigenvector]]
* Rank of a [[greedoid]], the maximal size of a feasible set
* [[Rank of a group]], the smallest cardinality of a generating set for the group
* Rank of a Lie group – see [[Cartan subgroup]] 
* Rank of a [[matroid]], the maximal size of an independent set
* [[Rank of a partition]], at least two definitions in number theory
* Rank of a [[tensor]]
* Rank of a [[vector bundle]]
* [[Rank statistics]]

==Other==
* [[Taxonomic rank]], in biology

==See also==
{{Wiktionary|rank}}
{{EB1911 poster|Rank}}
{{wikiquote}}
* {{in title|rank}}
* [[Ranking]]

[[Category:Ranks]]