Mathematical vector basis refers to two non-zero vectors e 1 and e2, which can represent any vector a in plane geometry. On the plane, any vector a (including zero vector) can be represented by two non-zero vectors (e 1, e2), that is, a=xe 1+ye2(x, y is any real number). This is the main content of the basic theorem of plane vector. The two nonzero vectors e 1 and e2 used to represent vector a are called a set of bases of vector a. ..

The basis vector cannot be a zero vector, that is, e 1≠0 and e2≠0 (where 0 represents a zero vector); A set of bases is not a non-zero vector, but two non-zero vectors. When vector a is represented by cardinality e 1 and e2, the values of real numbers x and y are unique. When the cardinality is e 1 and e2, there is only one real number (x, y), so a = xe1+ye2; It can be said that the basis of vector a is not unique. The bases e 1 and e2 can represent the vector a as a=xe 1+ye2, and a group of bases f 1 and f2 can also represent the vector a as a=mf 1+nf2.