K^n/Standard basis/Dual basis/Example

For the standard basis ${}e_{1},\ldots ,e_{n}$ of ${}K^{n}$, the dual basis consists in the projections onto some component, that is, we have ${}e_{i}^{*}=p_{i}$, where

$p_{i}\colon K^{n}\longrightarrow K,\left(x_{1},\,\ldots ,\,x_{n}\right)\longmapsto x_{i}.$

This basis is called the standard dual basis.