Rank

A rank is a position in a hierarchy. It can be formally recognized&mdash;for example, cardinal, chief executive officer, general, professor&mdash;or unofficial.

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 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