[Physics] How to know if something is a Lorentz transformation

inertial-framesmetric-tensorspecial-relativity

I'm studying special relativity and was wondering, if someone were to give me a matrix, is there a way or a procedure to check if that matrix corresponds to a Lorentz transformation? Even if the matrix contains projectors or other weird things?

Best Answer

Yes, it needs to leave the Minkowski metric invariant: $$ \Lambda^T\eta\Lambda=\eta. $$