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A simple theorem on proportionality of indefinite real quadratic forms isproved, and is used to clarify the proof of the invariance of the interval inSpecial Relativity from Einstein's postulate on the universality of the speedof light; students are often rightfully confused by the incomplete or incorrectproofs given in many texts. The result is illuminated and generalized usingHilbert's Nullstellensatz, allowing one form to be a homogeneous polynomialwhich is not necessarily quadratic. Also a condition for simultaneousdiagonalizabilityof semi-definite real quadratic functions is given.

Indefinite quadratic forms and the invariance of the interval in Special Relativity