Kronecker delta

$\delta_{ij}=1$ if $i=j$ , else $0$ -- the index-notation stand-in for the identity matrix.

The Kronecker delta $\delta_{ij}$ equals $1$ when $i=j$ and $0$ otherwise. In index notation it plays the role the identity matrix plays in matrix notation, and its summed (contracted) form $\delta_{ii}$ (in $n$ dimensions) equals $n$ , the trace of the identity.

Examples

$\delta_{11}=1$ , $\delta_{12}=0$ , $\delta_{33}=1$ .