Let $V$ be a finite-dimensional [vector space](/page/Vector%20Space) over a field $k$. Let $\mathcal B=(e_1,\ldots,e_n)$ be an ordered basis of $V$, and let $\mathcal B^*=(e_1^*,\ldots,e_n^*)$ be the [dual basis](/theorems/414) of $V^*$, characterized by