Dependence relation

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

A (binary) relation

between an element

and a subset

is called a dependence relation, written

, if it satisfies the following properties: Given a dependence relation

, a subset

is said to be independent if

is said to span

is said to be a basis of

is independent and

spans

is a non-empty set with a dependence relation

always has a basis with respect to

have the same cardinality.

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