The Kronecker Delta δij satisfies the following property:
where i and j are integers. For a summation:
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,
where the definition of matrix multiplication and the above property of summation was used.
The continuous analogue of Kronecker Delta is Dirac delta.
Weisstein, Eric W. "Kronecker Delta." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/KroneckerDelta.html