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## Main Question or Discussion Point

Hi.

The book I am using gives the following equations for the the Lorentz transformations of contravariant and covariant vectors

x

x

where the 2 Lorentz transformation matrices are the inverses of each other. I am trying to get equation 2 from equation 1 but if I lower the index on the LHS of (1) using the metric g

x

Then i'm stuck because how can I lower the ν on x

Thanks

The book I am using gives the following equations for the the Lorentz transformations of contravariant and covariant vectors

x

^{/μ}= Λ^{μ}_{ν}x^{ν}( 1 )x

_{μ}^{/}= Λ_{μ}^{ν}x_{v}( 2 )where the 2 Lorentz transformation matrices are the inverses of each other. I am trying to get equation 2 from equation 1 but if I lower the index on the LHS of (1) using the metric g

_{ρμ}and apply it to both sides of (1) I getx

_{ρ}^{/}= Λ_{ρν}x^{ν}Then i'm stuck because how can I lower the ν on x

^{ν}as ν is already repeated twice on the RHS and so I can't use a metric with ν in it ?Thanks