- #1

- 632

- 39

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 get

x

_{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