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»