So I have an issue understanding how to compute a matrix using the Minkowski metric as a null (read light-like) spacetime vector. As best I can understand it, it is a vector which has all velocity in the spacial components and none in time. Also, would a vector that transcends the speed of light mean that you are traveling through negative time? I don't really get how I should interpret a vector that is inside the light cone. So I have [-1 0 0 0] [0 1 0 0 ] [0 0 1 0 ] [0 0 0 1 ] for my matrix denoting the Minkowski metric (probably using wrong terminology) what would a vector that determines a null vector be?