_x²₁_ + _x²₂_ + _x²₃_ + _x²₄_ is changed into the quadratic for _m_ ∑
α_{_hk_} _x__{_h_}′ _x__{_k_}′,
where α_{_hk_} = α_{1_k_} α_{1_k_} + α_{2_h_} α_{2_k_} + α_{3_h_}
α_{3_k_} + α_{4_h_} α_{4_k_} are the members of a 4 × 4 series matrix
which is the product of Ā A, the transposed matrix of A into A. If by
the transformation, the expression is changed to
_x′₁²_ + _x₂′_^2 + _x₃′_^2 + _x′₄²_,
we must have Ā A = 1.
A has to correspond to the following relation, if transformation (38) is
to be a Lorentz-transformation. For the determinant of A) it follows out
of (39) that (Det A)² = 1, or Det A = ± 1.