$\begin{aligned} \boldsymbol{e}_{1}&=(1,0,0, \ldots, 0,0), \\ \boldsymbol{e}_{2}&=(0,1,0, \ldots, 0,0), \\ \vdots\\ \boldsymbol{e}_{n}&=(0,0,0, \ldots, 0,1) \end{aligned}$ A [[basis for vector space]] of dimension $n$ Typically [[coordinates]] are given in this basis, but sometimes it is necessary to express [[coordinate with respect to basis]]