A 4 × 4 series matrix 62) S = | S₁₁ S₁₂ S₁₃ S₁₄ | = | Skh |
| S₂₁ S₂₂ S₂₃ S₂₄ |
| S₃₁ S₃₂ S₃₃ S₃₄ |
| S₄₁ S₄₂ S₄₃ S₄₄ |
with the condition that in case of a Lorentz transformation it is to be replaced by ĀSA, may be called a space-time matrix of the II kind. We have examples of this in:—
1) the alternating matrix f, which corresponds to the space-time vector of the II kind,—
2) the product fF of two such matrices, for by a transformation A, it is replaced by (A⁻¹fA·A⁻¹FA) = A⁻¹fFA,
3) further when (ω₁, ω₂, ω₃, ω₄) and (Ω₁, Ω₂, Ω₃, Ω₄) are two space-time vectors of the 1st kind, the 4 × 4 matrix with the element Shk = ωhΩk,
lastly in a multiple L of the unit matrix of 4 × 4 series in which all the elements in the principal diagonal are equal to L, and the rest are zero.
We shall have to do constantly with functions of the space-time point (x, y, z, it), and we may with advantage