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I'm just wondering if the metric tensor (in its matrix form of 1 and -1's along the diagonal) is the same even when the direction of velocity of the "moving" frame isn't along the x-axis of the "stationary" frame but is in some arbitrary direction. This would obviously alter the Lorentz transformation matrix but it would seem to me that the metric tensor wouldn't change but I'm not sure. I'm just talking special relativity here so we don't need to generalize anything to general relativity. I'd appreciate any help. Thanks