Relativity
The Special and General Theory

by a new system with its axes pointing in other directions.

Mathematically, we can characterize the generalized Lorentz transformation thus:

It expresses x', y', z', t', in terms of linear homogeneous functions of x, y, z, t, of such a kind that the relation

x'2 + y'2 + z'2 - c2t'2 = x2 + y2 + z2 - c2t2

(11a)

is satisfied identically. That is to say: If we substitute their expressions in x, y, x, t, in place of x', y', z', t', on the left-hand side, then the left-hand side of (11a) agrees with the right-hand side.