In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.

be a set and a subset is called a dependence relation, if it satisfies the following properties:

1. ;

2. , then there is a finite;

3. ;

4. .

Given a dependence relation is said to be independent is said to span is said to be a basis is independent spans

have the same cardinality.

, using property 3. and 1.

Examples

• be a vector space over a field is in the subspace, is a dependence relation. This is equivalent to the definition of linear dependence.

• be a field extension is algebraic is a dependence relation. This is equivalent to the definition of algebraic dependence.

See also

• matroid

References