Kronecker delta

Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise

In mathematics, the Kronecker delta (named after Leopold Kronecker), is a function of two variables, usually non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j = { 0 if i ≠ j , 1 if i = j . {\displaystyle \delta _{ij}={\begin{cases}0&{\text{if }}i\neq j,\\1&{\text{if }}i=j.\end{cases}}} or with use of Iverson brackets: δ i j = [ i = j ] {\displaystyle \delta _{ij}=[i=j]\,} For example, δ 12 = 0 {\displaystyle \delta _{12}=0} because 1 ≠ 2 {\displaystyle 1\neq 2} , whereas δ 33 = 1 {\displaystyle \delta _{33}=1} because 3 = 3 {\displaystyle 3=3} .

From Wikipedia, under CC BY-SA. More on occurri.