Kronecker Delta

linear-algebra

Definition

Kronecker Delta

The Kronecker delta is a function $\delta :I\times I\to \{0,1\}$ defined on an index set $I$ (typically $\mathbb{N}$ or $\mathbb{Z}$):

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

In matrix form, ${\delta }_{ij}$ represents the entries of the identity matrix $I$:

$$(I{)}_{ij}={\delta }_{ij}$$