Editing Dual basis (section)

===Finite-dimensional vector spaces===

In the case of finite-dimensional vector spaces, the dual set is always a dual basis and it is unique. These bases are denoted by <math>B=\{e_1,\dots,e_n\}</math> and <math>B^*=\{e^1,\dots,e^n\}</math>. If one denotes the evaluation of a covector on a vector as a pairing, the biorthogonality condition becomes:
:<math>\left\langle e^i, e_j \right\rangle = \delta^i_j.</math>

The association of a dual basis with a basis gives a map from the space of bases of ''V'' to the space of bases of ''V''<sup>∗</sup>, and this is also an isomorphism. For [[topological field]]s such as the real numbers, the space of duals is a [[topological space]], and this gives a [[homeomorphism]] between the [[Stiefel manifold]]s of bases of these spaces.