dual basis map dimension linear maps linearly independent similar basis
If v1, ..., vn is a basis of V (this implies that V is finite-dimensional), then one can define, for i = 1, ..., n, a linear map vi* such that vi*(vi) = 1 and vi*(vj) = 0 if j ≠ i. These linear maps form a basis of V*, called the dual basis of v1, ..., vn. (If V is not finite-dimensional, the vi* may be defined similarly; they are linearly independent, but do not form a basis.)
