A rank is a position in a hierarchy. It can be formally recognized—for example, cardinal, chief executive officer, general, professor—or unofficial.
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 an elliptic curve 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 Rank (J programming language)
See also
Ranking