Standard Basis

Definition: Standard Basis

The standard basis of the vector space $(F^n,F,+,\cdot )$ of column vectors in $F^n$ is the ordered basis

$$\left(\underset{n\text{ vectors}}{\underbrace{{\vec{e}}_1=\left[\begin{array}{c}{1}_F\\ 0_F\\ ⋮\\ 0_F\end{array}\right],{\vec{e}}_2=\left[\begin{array}{c}{0}_F\\ 1_F\\ ⋮\\ 0_F\end{array}\right],\cdots ,{\vec{e}}_n=\left[\begin{array}{c}{0}_F\\ 0_F\\ ⋮\\ 1_F\end{array}\right]}}\right)$$