Kronecker Delta

#Physics #Math
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$$
\delta_{ij}=
\begin{cases}
0, & i=j \\1, & i\neq j
\end{cases}
$$

• 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

$a_j\delta_{jk}=a_k$

$\delta_{jj}=n$

• $\displaystyle n$ is the number of dimensions