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As known, any Lorentz transformation matrix

##\Lambda##

must obey the relation

##\Lambda^μ{}_v####\Lambda^ρ{}_σ##g

. The same holds also for the inverse metric tensor

g

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

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

Λ

, 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.

##\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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