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Description of the Lorentz transformation with a special scalar and skew-scalar product
1. Summary of antecedents
I wrote earlier1 that all the three number-plane one can define a special symplectic form in the same way:
ω(z1,z2) = Im(z̄1z2) = x1y2 – x2y1 (1)
This is equal to 0 if x1y2=x2y1 i.e. y1/x1=y2/x2, so if the two number-vectors are collinear.
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1 See «The "natural presences" of the symplectic camel»
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