Index notation of matrix tranpose

Zee writes in Einstein Gravity in a nutshell page 186

"let us define the transpose by ##(\Lambda^T)_\sigma^\mu = \Lambda_\sigma^\mu##"

and even emphasizes the position of the indexes. Yes, they are not exchanged! This must be a typo, right?

WannabeNewton
No, what he says is perfectly fine: he writes ##\Lambda^{\mu}{}{}_{\sigma} = (\Lambda^T)_{\sigma}{}{}^{\mu}## which is not what you wrote above.

And you are telling me now that this glitch in the typography of the slightly out of place indexes is the crucial point?

Oh my, I thought I understood why we have upper and lower indexes? But what is the meaning of an index slighly shifted to the right?

DrGreg
$$A_\lambda{}^\mu = g_{\lambda\nu} \, A^{\nu\mu} = g_{\lambda\nu} \, g^{\mu\sigma} \, A^\nu{}_\sigma$$