This is a fairly trivial question I think. I'm only asking it here because after some googling I was unable to find its answer. I was at one point led to believe that the form of the Lorentz-transformation matrix is dependent on the convention used for the Minkowski metric. Specifically it was my understanding that [γ, βγ, 0, 0] [βγ, γ, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1] was the transformation matrix when the West-coast metric, diag(1, -1, -1, -1), is used. This is the inverse of the more commonly encountered [γ, -βγ, 0, 0] [-βγ, γ, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1] which I know is correct at least for the East-coast metric, diag(-1, 1, 1, 1). I was working a problem recently and got a result using the former of these transformation matrices that was clearly incorrect. Does the Lorentz transformation's form actually depend on the convention for the metric, or did I concoct this entire distinction? Perhaps I misunderstood one of my professors.