Kronecker delta

The Kronecker delta ${\delta }_{ij}$ is defined as having value 1 when $i=j$ and 0 otherwise ($i$ and $j$ are integers). It may also be written as ${\delta }^{ij}$ or ${\delta }_j^i$. It is a special case of the generalized Kronecker delta symbol.

The delta symbol was first used in print by Kronecker in 1868[1].

Example.

The $n\times n$ identity matrix $I$ can be written in terms of the Kronecker delta as simply the matrix of the delta, $I_{ij}={\delta }_{ij}$, or simply $I=({\delta }_{ij})$.