(23) f₂₃(x₂y₃ - x₃y₂) + f₃₁(x₃y₁ - x₁y₃) + f₁₂(x₁y₂
- x₂y₁) + f₁₄(x₁y₄ - x₄y₁) + f₂₄(x₂y₄ - x₄y₂) +
f₃₄(x₃y₄ - x₄y₃)
with six coefficients f₂₃--f₃₄. Let us remark that in the vectorial method of writing, this can be constructed out of the four vectors.
x₁, x₂, x₃; y₁, y₂, y₃; f₂₃, f₃₁, f₁₂; f₁₄, f₂₄, f₃₄ and the constants x₄ and y₄, at the same time it is symmetrical with regard the indices (1, 2, 3, 4).
If we subject (x₁, x₂, x₃, x₄) and (y₁, y₂, y₃, y₄) simultaneously to the Lorentz transformation (21), the combination (23) is changed to:
(24) f₂₃′(x₂′y₃′ - x₃′y₂′) + f₃₁(x₃′y₁′ - x₁′y₃′) + f₁₂
(x₁′y₂′ - x₂′y₁′) + f₁₄′(x₁′y₄′) - x₄′y₁′) + f₂₄′(x₂′y₄′
- x₄′y₂′) + f₃₄′(x₃′y₄′ - x₄′y₃′),
where the coefficients f₂₃′, f₃₁′, f₁₂′, f₁₄′, f₂₄′, f₃₄′, depend solely on (f₂₃ f₂₄) and the coefficients a₁₁ ... a₄₄.