As known, any Lorentz transformation matrix(adsbygoogle = window.adsbygoogle || []).push({});

##\Lambda##

must obey the relation

##\Lambda^μ{}_v####\Lambda^ρ{}_σ##g_{μ}_{ρ}=g_{v}_{σ}

. The same holds also for the inverse metric tensor

g^{vσ}

which has the same components as the metric tensor itself (don't really understand why every tex formula starts from a new line), i.e.

##\Lambda^v{}_μ####\Lambda^ρ{}_σ##g^{vσ}=g^{μρ}

. Putting this all as a matrix relation, these two formulas are

Λ^{T}gΛ=g , ΛgΛ^{T}=g

, where g is the metric tensor (and also the inverse metric tensor, as they are both the same).

I dont understand why is the lambda transpose and why the two different metric tensor suddenly become the same g. Is there something that I am missing out? And I a bit unsure of the inverse metric tensor stated above.

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# Lorentz transformation

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