We have denoted the four-vector ω by the matrix | ω₁ ω₂ ω₃ ω₄ |. It is then at once seen that [=ω] denotes the reciprocal matrix
| ω₁ |
| ω₂ |
| ω₃ |
| ω₄ |
It is now evident that while ω¹ = ωA, [=ω]¹ = A⁻¹[=ω]
[ω, s] The vector-product of the four-vector ω and s may be represented by the combination
[ωs] = [=ω]s - ṡω
It is now easy to verify the formula f¹ = A⁻¹fA. Supposing for the sake of simplicity that f represents the vector-product of two four-vectors ω, s, we have
f¹ = [ω¹s¹] = [=ω]¹s¹ - [=s]1ω1]