Theorem 6.3 (Criterion for Lorentz Frames)

The following are equivalent:

(a) A coordinate system i in Minkowski space M is Lorentz at the point p

(b) If x is any frame such that, at p, G = diag[1, 1, 1, -c2], then the columns of the change-of-coordinate matrix

satisfy

where the inner product is defined by the matrix G.

(c) = diag[1, 1, 1, -c2]

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