Template:Individual-TLP-paragraph-en-6.241

6.241 Thus the proof of the proposition 2 × 2 = 4 runs:

[math]\displaystyle{ ( \Omega^{ \nu} )^{\mu \prime} x = \Omega^{ \nu \times \mu \prime} x \text{ Def.} }[/math]

[math]\displaystyle{ \Omega^{2 \times 2 \prime} x = (\Omega^2 )^{2 \prime} x = ( \Omega^2 )^{1+1 \prime} x = \Omega^{2 \prime} \Omega^{2 \prime} x = \Omega^{1 + 1 \prime} \Omega^{1 + 1 \prime} x }[/math]

[math]\displaystyle{ (\Omega ' \Omega)^{\prime} (\Omega ' \Omega)^{\prime} x = \Omega ' \Omega ' \Omega ' \Omega ' x = \Omega^{1 + 1 + 1 + 1 \prime} x = \Omega^{4 \prime} x }[/math]