Thank you very much, this really clears it up for me, you've been very helpful. So just to check, on the lhs we are thinking of eta not as a whole matrix, but are instead just considering the specific components given by mu and nu?
I really appreciate your help, thanks for your time but I'm still struggling to understand. I understand that the indices aren't being summed over, rather that the sum of the diagonal part of the gamma matrix is the trace. I'm still not understanding why the eta matrix can be moved inside the...
If it's a tensor not a scalar why can we put it inside the trace? Sorry if I'm missing something obvious. I thought the indices on the eta referred to the elements in eta and the trace is the sum of the diagonal elements and so the trace would also apply to the eta?
I'm reading through some lecture notes and there is a proof that the gamma matrices are traceless that I've never seen before (I've seen the "identity 0" on wikipedia proof) and I can't work out some of the steps:
\begin{align*}
2\eta_{\mu\nu}Tr(\gamma_\lambda) &=...
Sorry, I don't really understand what you mean by "dimension" in this case;
I know that the transpose of a 1x2 matrix should be a 2x1 matrix but I don't know whether the elements actually inside the matrix should be transposed once I make the matrix a 2x1.
Thank you in advance for any help.