Standard Basis

Definition

For the $n$-dimensional real vector space ${\mathbb{R}}^n$, the standard basis is defined as $\begin{array}{rl}{\mathbf{e}}_1& =(1,0,\dots ,0)\\ {\mathbf{e}}_2& =(0,1,\dots ,0)\\ & \dots \\ {\mathbf{e}}_n& =(0,0,\dots ,1)\end{array}$ Each ${\mathbf{e}}_i$ is a vector with $1$ in the $i$-the position and $0$ in all the other positions.