Let V {\displaystyle {}V} be a finite-dimensional K {\displaystyle {}K} -vector space, endowed with a basis v 1 , … , v n {\displaystyle {}v_{1},\ldots ,v_{n}} , and the corresponding dual basis
v ∈ V {\displaystyle {}v\in V} , the equality
The linear forms v i ∗ {\displaystyle {}v_{i}^{*}} yield the scalars (coordinates) of a vector with respect to a basis.