Identity matrix

Definition

A matrix $I\in R^{n\times n}$ is said to be a identity matrix if it is in the form of

$$I={\left[\begin{array}{cccc}1& 0& \dots & 0\\ 0& 1& \dots & 0\\ ⋮& ⋮& ⋮& ⋮\\ 0& 0& \dots & 1\end{array}\right]}_{n\times n}$$

where $i_{ii}=1$ and $i_{ij}=0$ if $i\ne j$.