I'm having difficulty in deriving the commutation relation:
[Eij, Ekl] = $\delta$jk Eil - $\delta$il Ekj
Here Eij is a matrix with null entries everywhere at the i'th row and j'th column, where it is 1. Can someone help me please? Thanks
2026-04-27 19:11:39.1777317099
Derive the commutation relation
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If I understand the notation correctly, $E_{ij}$ is a matrix with entries zero except the $ij$ entry which is one. Therefore, the $ab$ component of the product of two such matrices is $$(E_{ij}E_{kl})_{ab}=\sum_t (E_{ij})_{at}(E_{kl})_{tb}=\sum_t \delta_{ia}\delta_{jt}\delta_{kt}\delta_{lb}=\delta_{ia}\delta_{jk}\delta_{lb}=\delta_{jk}(E_{il})_{ab}$$
and likewise for the commuted product, leading to the commutator by making the difference.