Kronecker delta

The Kronecker delta (Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \delta _{ij}} ) is as the discrete version of the Dirac delta distribution defined by

$\delta _{ij}=\left\{{\begin{array}{lll}0&{\rm {for}}~i\neq j\\1&{\rm {for}}~i=j\end{array}}\right.$