# Kronecker delta

In algebra, the **Kronecker delta** is a notation for a quantity depending on two subscripts *i* and *j* which is equal to one when *i* and *j* are equal and zero when they are unequal:

If the subscripts are taken to vary from 1 to *n* then δ gives the entries of the *n*-by-*n* identity matrix. The invariance of this matrix under orthogonal change of coordinate makes δ a rank two tensor.

Kronecker deltas appear frequently in summations where they act as a "filter". To clarify this we consider a simple example

that is, the element *S*_{4} is "sifted out" of the summation by δ_{i,4}.

In general, (*i* and *a* integers)

The Kronecker delta is named after the German mathematician Leopold Kronecker (1823 – 1891). See Dirac delta function for a generalization of the Kronecker delta to real *i* and *j*.