1. The problem statement, all variables and given/known data Find Fμν, given Fμν= (0 Ex Ey Ez) (-Ex 0 Bz -By) (-Ey -Bz 0 -Bx) (-Ez By -Bx 0) 2. Relevant equations gμν = Diag( -1, 1, 1, 1) 3. The attempt at a solution I tried computing Fμν = gμνFμν but this gave (0 -Ex -Ey -Ez) (-Ex 0 Bz -By) (-Ey -Bz 0 Bx) (-Ez By -Bx 0) Which seems wrong to me, since the next question is to find FμνFνμ and this is meant to come out as the Lagrangian and from my notes I don't see this working. I think I'm messing up my index notation, I think I may need an extra metric in there because there are 2 indices downstairs but I don't have the best understanding. Any help and advice on dealing with pesky index notation would be greatly appreciated, Thanks!