Kronecker Delta

Universal Danker Video
Universal Danker PDF

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

• The definition of the Kronecker Delta. It is analogous to the identity matrix in linear algebra

Properties

${\delta }_{ij}={\delta }_{ji}$

• Indices can swap

${\delta }_{ij}{\delta }_{jk}={\delta }_{ik}$

• Collapse in Einstein notation

$a_j{\delta }_{jk}=a_k$

${\delta }_{jj}=n$

• $n$ is the number of dimensions