The standard [[Basis]] for a [[Coordinate System]] of $\R^n$ is the [[Set]] of [[Vector|Vectors]] composing the [[Identity Matrix]] of $\R^n$. >[!example] >$ >\mathcal S_{3} >= \left\{\vec e_{1}, \vec e_{2}, \vec e_{3}\right\} >= \left\{ >\mat{1\\ 0\\0}\\ , >\mat{1\\ 0\\0}\\ , >\mat{1\\ 0\\0}\\ , >\mat{1\\ 0\\0}\\ \right\} >$