A rank is a position in a

hierarchy A hierarchy (from Ancient Greek, Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy ...

. It can be formally recognized—for example,

cardinal Cardinal or The Cardinal most commonly refers to * Cardinalidae, a family of North and South American birds **''Cardinalis'', genus of three species in the family Cardinalidae ***Northern cardinal, ''Cardinalis cardinalis'', the common cardinal of ...

chief executive officer A chief executive officer (CEO), also known as a chief executive or managing director, is the top-ranking corporate officer charged with the management of an organization, usually a company or a nonprofit organization. CEOs find roles in variou ...

general A general officer is an Officer (armed forces), officer of high rank in the army, armies, and in some nations' air force, air and space forces, marines or naval infantry. In some usages, the term "general officer" refers to a rank above colone ...

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

—or unofficial.

People

Formal ranks

Academic rank Academic rank (also scientific rank) is the rank of a scientist or teacher in a college, high school, university or research establishment. The academic ranks indicate relative importance and power of individuals in academia. The academic ran ...

Corporate title Corporate titles or business titles are given to corporate officers to show what duties and responsibilities they have in the organization. Such titles are used by publicly and privately held for-profit corporations, cooperatives, non-profit org ...

Diplomatic rank Diplomatic rank is a system of professional and social rank used in the world of diplomacy and international relations. A diplomat's rank determines many ceremonial details, such as the order of precedence at official processions, Seating plan, t ...

Hierarchy of the Catholic Church The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means the "holy ordering" of the church, the Body of Christ, so to respect the diversity of gif ...

Imperial, royal and noble ranks Traditional rank amongst European emperor, imperiality, monarch, royalty, peerage, peers, and nobility is rooted in Late Antiquity and the Middle Ages. Although they vary over time and among geographic regions (for example, one region's prince ...

Military rank Military ranks is a system of hierarchy, hierarchical relationships within armed forces, police, Intelligence agency, intelligence agencies, paramilitary groups, and other institutions organized along military organisation , military lines, such ...

* Police rank

Unofficial ranks

Social class A social class or social stratum is a grouping of people into a set of Dominance hierarchy, hierarchical social categories, the most common being the working class and the Bourgeoisie, capitalist class. Membership of a social class can for exam ...

Social position Social position is the position of an individual in a given society and culture. A given position (for example, the occupation of ''priest'') may belong to many individuals. Definition Stanley Wasserman and Katherine Faust Stanley cautioned ...

Social status Social status is the relative level of social value a person is considered to possess. Such social value includes respect, honour, honor, assumed competence, and deference. On one hand, social scientists view status as a "reward" for group members ...

Either

Seniority Seniority is the state of being older or placed in a higher position of status relative to another individual, group, or organization. For example, one employee may be senior to another either by role or rank (such as a CEO vice a manager), or by ...

Mathematics

Rank (differential topology) In mathematics, the rank of a differentiable map f:M\to N between differentiable manifolds at a point p\in M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map :d_p f : T_p M \to T_N\, from the tangent ...

Rank (graph theory) In graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up ...

Rank (linear algebra) In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. p. 48, § 1.16 This corresponds to the maximal number of linearly independent columns of . This, in turn, is identical to the di ...

, the dimension of the vector space generated (or spanned) by a matrix's columns *

Rank (set theory) In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by ''V'', is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory ( ...

* Rank (type theory) *

Rank of an abelian group In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group ''A'' is the cardinality of a maximal linearly independent subset. The rank of ''A'' determines the size of the largest free abelian group contained in ''A''. If '' ...

, the cardinality of a maximal linearly independent subset * Rank of a

free module In mathematics, a free module is a module that has a ''basis'', that is, a generating set that is linearly independent. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commu ...

* Rank of a

greedoid In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Hassler Whitney, Whitney in 1935 to study planar graphs and was later used by Jack Edmonds, Edmonds to characterize ...

, the maximal size of a feasible set *

Rank of a group In the mathematical subject of group theory, the rank of a group ''G'', denoted rank(''G''), can refer to the smallest cardinality of a generating set for ''G'', that is : \operatorname(G)=\min\. If ''G'' is a finitely generated group, then the ...

, the smallest cardinality of a generating set for the group * Rank of a Lie group – see

Cartan subgroup In the theory of algebraic groups, a Cartan subgroup of a connected linear algebraic group G over a (not necessarily algebraically closed) field k is the centralizer of a maximal torus. Cartan subgroups are smooth (equivalently reduced), connec ...

* Rank of a

matroid In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

, the maximal size of an independent set *

Rank of a partition In number theory and combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this ar ...

, at least two definitions in number theory * Rank of a

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

* Rank of a

vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to eve ...

Rank statistics In statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying s ...

Other

Taxonomic rank In biology, taxonomic rank (which some authors prefer to call nomenclatural rank because ranking is part of nomenclature rather than taxonomy proper, according to some definitions of these terms) is the relative or absolute level of a group of or ...

, in biology

People

Formal ranks

Unofficial ranks

Either

Mathematics

Other

See also