In a recent course on special relativity the lecturer derives the Lorentz transformation matrix for the four vector of position and time. Then, apparently without proof, the same matrix is used to transform the EM field tensor to the tensor for the new inertial frame. I am unclear whether it should be obvious (if so why?) that the two are the same or whether the proof is non trivial (sketch of proof would help) and was just omitted. Thank you.