06 - Kronecker Delta

Kronecker Delta

$${\delta }_{ij}=\{\begin{array}{ll}1& \text{ if }i=j\\ 0& \text{ if }i\ne j\end{array}$$

Sifting Property of the Kronecker Delta

Let $x_1,x_2,\cdots ,x_n$ be $n$ real numbers
Then for $1\le k\le n$

$$\sum _{i=1}^n{x}_i{\delta }_{ik}=x_k$$

Allows you to select (sift) the $k$th element from a list of numbers