Kronecker delta

In algebra, the Kronecker delta is a notation $\delta _{ij}$ 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:

$\delta _{ij}={\begin{cases}1&\quad \mathrm {if} \quad i=j\\0&\quad \mathrm {if} \quad i\neq j.\end{cases}}$

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.