~ Kronecker delta

The Kroenecker delta is a function of two indices that returns the corresponding element of the identity matrix. It is defined as¹:

$$\delta_{ij} \equiv \begin{cases}1, & i = j \\ 0, & i \ne j\end{cases}$$

Using index notation, the Kroenecker delta can be represented in these ways:

$$\delta_{ij} \equiv \delta_j^i \equiv \delta^{ij}$$