Lorentz transformation, quantum field theory

[M. next]

Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g$_{ρσ}$=g$_{μ\upsilon}$$\Lambda$$^{μ}$$_{ρ}$$\Lambda$$^{\upsilon}$$_{σ}$.

My question is what do I need from tensor calculus to get how did he jump between (1.2.20), (1.2.21), (1.2.22)? Thank you

 

[dextercioby]

Just knowledge on how to manipulate contracted products.