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:

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

1

Weisstein, E. W. (n.d.). Kronecker Delta. MathWorld--A Wolfram Web Resource. Retrieved May 26, 2021, from https://mathworld.wolfram.com/KroneckerDelta.html

12:55 Wednesday 26 May 2021