K^n/Standard basis/Dual basis/Example

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

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

This basis is called the standard dual basis.