employ the 1 × 4 series matrix, formed of differential symbols,—
| ∂/∂x, ∂/∂y, ∂/∂z, ∂/i∂t,|
or (63) | ∂/∂x₁ ∂/∂x₂ ∂/∂x₃ ∂/∂x₄ |
For this matrix I shall use the shortened from “lor.”[[25]]
Then if S is, as in (62), a space-time matrix of the II kind, by lor S′ will be understood the 1 × 4 series matrix
| K₁ K₂ K₃ K₄ |
where Kk = ∂S1k/∂x₁ + ∂S2k/∂x₂ + ∂S3k/∂x₃ + ∂S4h/∂x₄.
When by a Lorentz transformation A, a new reference system (x′₁ x′₂ x′₃ x₄) is introduced, we can use the operator
lor′ = | ∂/∂x₁′ ∂/∂x₂′ ∂/∂x₃′ ∂/∂x₄′ |
Then S is transformed to S′= Ā S A = | S′hk |, so by lor 'S′ is meant the 1 × 4 series matrix, whose element are