[½ (m M - eE)²] + (em) (EM),
is >= 0, because (em = ε Φ [=ψ], (EM) = μ Φ [=ψ]; now referring back to 79), we can denote the positive square root of this expression as Det1/4 S.
Since ḟ = -f, and Ḟ = -F, we obtain for Ṡ, the transposed matrix of S, the following relations from (78),
(84) Ff = Ṡ - L, f* F* = -Ṡ - L,
Then is
Ṡ - S = | Sh k - St k |
an alternating matrix, and denotes a space-time vector of the second kind. From the expressions (83), we obtain,
(85) S - Ṡ = - (εμ - 1) [ω, Ω],
from which we deduce that [see (57), (58)].
(86) ω (S - Ṡ)* = 0,