09 - Standard Basis of Matrices

Standard Basis for $M_{mn}$

For $1\le I\le m$ and $1\le J\le n$ then

$E_{ij}$ is the matrix with $1$ in the $(i,j)$th entry and $0$ elsewhere
So

$$(i,j)\text{th}\text{ entry of }{E}_{IJ}={\delta }_{Ii}{\delta }_{Jj}$$