What's the relation between $\delta_{ij}$ and $\delta_{ji}$?
What about their mathematical and physical meanings?
Thank you!
What's the relation between $\delta_{ij}$ and $\delta_{ji}$?
What about their mathematical and physical meanings?
Thank you!
It appears from the comments that you are referring to the Kronecker delta, $\delta_{ij} = \begin{cases}1, & i=j \\ 0, & \textrm{else.}\end{cases}$ An immediate consequence of the definition above is that the Kronecker delta is symmetric, $\delta_{ij} = \delta_{ji}$.
One can think of $\delta_{ij}$ as the $ij$th component of the identity matrix, $I$. Since $I^T = I$, $\delta_{ij} = I_{ij} = (I^T)_{ij} = I_{ji} = \delta_{ji}.$ It is natural to interpret the Kronecker delta as the Euclidean metric.