i.e. the reciprocal matrix of A is equivalent to the transposed matrix of A.
For A as Lorentz transformation, we have further Det A = +1, the quantities involving the index 4 once in the subscript are purely imaginary, the other co-efficients are real, and a₄₄ > 0.
5⁰. A space time vector of the first kind[[21]] which s represented by the 1 × 4 series matrix,
(41) s = |s₁ s₂ s₃ s₄|
is to be replaced by sA in case of a Lorentz transformation
A. i.e. s′ = | s₁′ s₂′ s₃′ s₄′| = |s₁ s₂ s₃ s₄| A;
A space-time vector of the 2nd kind[[22]] with components f₂₃ ... f₃₄ shall be represented by the alternating matrix
(42) f = | 0 f₁₂ f₁₃ f₁₄ |
|f₂₁ 0 f₂₃ f₂₄ |
|f₃₁ f₃₂ 0 f₃₄ |