Kronecker delta - Knowlpedia

The Kronecker delta is the symbol

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

It tests equality of the indices. The indices are often natural numbers, but the same definition works on any specified index set.

Finite sums

For indices $i,j\in\{1,\ldots,n\}$ , the matrix $(\delta_{ij})$ is the identity matrix, and $\sum_j\delta_{ij}v_j=v_i$ . This discrete symbol is different from the Dirac delta distribution.