In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.
Let be a set. A (binary) relation between an element of and a subset of is called a dependence relation, written , if it satisfies the following properties:
Given a dependence relation on , a subset of is said to be independent if for all If , then is said to span if for every is said to be a basis of if is independent and spans
Remark. If is a non-empty set with a dependence relation , then always has a basis with respect to Furthermore, any two bases of have the same cardinality.
This article incorporates material from Dependence relation on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.