# Kronecker Delta

The Kronecker Delta δij satisfies the following property:

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

where i and j are integers. For a summation:

$\sum_{i=-\infty}^\infty c_i \delta_{ij} =c_j$.

The elements of the identity matrix can be seen as following Kronecker Delta (i.e, (I)ij = δij). To see this, let A be an nxn matrix, aij be its elements and I be the nxn identity matrix. Then A = AI so,

$a_{ij} = \sum_{k=0}^n a_{ik}(I)_{kj} = \sum_{k=0}^n a_{ik}\delta_{kj} = a_{ij}$

where the definition of matrix multiplication and the above property of summation was used.

The continuous analogue of Kronecker Delta is Dirac delta.

## References

Weisstein, Eric W. "Kronecker Delta." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/KroneckerDelta.html