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

Let $V$ be a finite-dimensional $K$-vector space, endowed with a basis $v_1,\dots ,v_n$.

Then the

dual basis

$v_1^{\ast },\dots ,v_n^{\ast }\in V^{\ast }$

is a basis of the

dual space.

Proof, Write another proof