Rank Symmetric
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Rank Symmetric
A rank is a position in a hierarchy. It can be formally recognized—for example, Cardinal (Catholic Church), cardinal, chief executive officer, General 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 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 maxi ...
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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 is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science, organizational theory, systems theory, systematic biology, and the social sciences (especially political science). A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path (graph theory), path. All parts of the hierarchy that are ...
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