ωf = | if₄₁, if₄₂, if₄₃, 0 |;
ωf* = | if₃₂, if₁₃, if₂₁, 0 |
[ω · ωf] = 0, 0, 0, f₄₁, f₄₂, f₄₃;
[ω · ωf*]* = 0, 0, 0, f₃₂, f₁₃, f₂₁.
The fact that in this special case, the relation is satisfied, suffices to establish the theorem (45) generally, for this relation has a covariant character in case of a Lorentz transformation, and is homogeneous in (ω₁, ω₂, ω₃, ω₄).
After these preparatory works let us engage ourselves with the equations (C,) (D,) (E) by means which the constants ε μ, σ will be introduced.
Instead of the space vector u, the velocity of matter, we shall introduce the space-time vector of the first kind ω with the components.
ω₁ = ux/√(1 - u²),
ω₂ = uy/√(1 - u²),
ω₃ = uz/√(1 - u²),