Standard Basis Matrix

This is a matrix $E^{i,j}$ where a $1$ is placed on every $(i,j)$ cell starting with $i=0$.

Example

0 & 0 & 0& 0& 0& 0& \dots\\ 1 & 0 & 0& 0& 0& 0& \dots\\ 0 & 1 & 0& 0& 0& 0& \dots\\ 0 & 0 & 1& 0& 0& 0& \dots\\ 0 & 0 & 0& 1& 0& 0& \dots\\ \vdots \end{array}\right]$$