Let R be the real numbers and V be a vector space over R. The set of vectors {v1,v2,...,vn} is said to form abasiswhen any vector in V can be expressed* in terms of v_1,v_2,...,v_n AND in only one way.

For example, is a basis for over . Because anything in can be expressed in terms of those.

*)By "expressed" I mean as a linear combination of those vectors.