Page:Grundgleichungen (Minkowski).djvu/37

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For this matrix I shall use the shortened from lor.

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

where

(64)

When by a Lorentz transformation , a new reference system is introduced, we can use the operator

Then S is transformed to , so by lor' Sis meant the 1✕4 series matrix, whose element are

Now for the differentiation of any function of (x y z t) we have the rule

,

so that, we have symbolically

Therefore it follows that

(65) ,

i.e., lor S behaves like a space-time vector of the first kind.

If L is a multiple of the unit matrix, then by lor L will be denoted the matrix with the elements