Encyclopedia
Rank
Position in a hierarchy
A rank is a position in a hierarchy. It can be formally recognized, for example, cardinal, chief executive officer, general, professor, or unofficial.
01People
Formal ranks
- Academic rank
- Corporate title
- Diplomatic rank
- Hierarchy of the Catholic Church
- Imperial, royal and noble ranks
- Military rank
- Police rank
Unofficial ranks
Either
02Mathematics
- 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
03Other
- Taxonomic rank, in biology
- Rank (J programming language)
Sources and credits
This article is adapted from the Wikipedia article “Rank”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- 1st sergeant.JPG by C Phillips96, CC BY-SA 3.0
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