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

[ω_s_] = [=ω]_s_ - _ṡ_ω

It is now easy to verify the formula _f_¹ = A⁻¹_f_A. Supposing for the

sake of simplicity that _f_ represents the vector-product of two

four-vectors ω, _s_, we have

_f¹_ = [ω¹_s¹_] = [[=ω]¹_s¹_ - [=_s_]^1ω^1]

= [A⁻¹ [=ω]_s_A - A⁻¹_s_[=ω]A]

= A⁻¹[[=ω]_s_ - _s_[=ω]]A = A⁻¹_f_A.