Finite-dimensional vector space/Dual basis/Basis/Fact

Let ${}V$ be a finite-dimensional ${}K$-vector space, endowed with a basis ${}v_{1},\ldots ,v_{n}$.

Then the

dual basis

${}v_{1}^{*},\ldots ,v_{n}^{*}\in {V}^{*}\,$

is a basis of the

dual space.

Proof, Write another proof