(66) |

If is a space-time vector of the 1st kind, then

(67) |

In case of a Lorentz transformation , we have

*i.e.*, *lor s* *is an invariant in a {sc|Lorentz}}-transformation.*

*In all these operations the operator* lor *plays the part of a space-time vector of the first kind.*

If *f* represents a space-time vector of the second kind, *-lor f* denotes a space-time vector of the first kind with the components

So the system o£ differential equations (A) can be expressed in the concise form

{A} |

and the system (B) can be expressed in the form

{B} |

Referring back to the definition (67) for , we find that the combinations and vanish identically, when *f* and *F** are alternating matrices. Accordingly it follows out of (A), that

(68) | , |