The term characteristic in mathematics typically stands for:
- Something specific, unique, intrinsic or invariant to the situation
- Something that completely describes the given situation
Related terms are invariant.
In commutative algebra/field theory
Characteristic of a ring: The smallest positive integer such that . If no such positive integer exists, then the characteristic is said to be zero. A field either has characteristic zero or has characteristic equal to a prime number.
In group theory
Characteristic subgroup: A subgroup that is invariant (or, gets mapped to itself) under any automorphism of the group.
In algebraic topology/differential geometry
Characteristic class: A natural transformation from the vector bundle functor to the cohomology functor on a manifold; in other words, it assigns to every vector bundle over a manifold, a cohomology class, such that a certain naturality diagram commutes.
In measure theory/analysis
Characteristic function of a set, also called its indicator function, is a function that takes value 1 on the set and 0 outside it.