It's kind of funny because one of the first things the prof does in Lecture 1 of that class is tell his students that yes you're going to feel in your soul that you should treat these early rank 2 tensors (like the Minkowski metric ##\eta_{\alpha\beta}## or Lorentz transform...
Or does this even really matter since the formulas used in this course will be in terms of components instead of matrices so who cares whether it's ##\alpha## or ##\mu'## that gives the row index of the matrix representation of the ##\binom{1}{1}## tensor ##L^\alpha_{\phantom{\alpha}\mu'}##?
I have been following the 8.962 class on OCW and I was thinking I was writing out the components correctly with first index row, second index column like matrices have been written in every other course I have taken, and pretty much every example we have gone through in the class in the first...