If I have a (1,1) tensor, eg a Lorentz transform, how do I write its inverse? For example:
[tex]x'^\mu=\Lambda^\mu_\nu x^\nu[/tex]
Would I multiply on the left by:
[tex](\Lambda^{-1})^\nu_\mu[/tex]?
It seems to make sense, but I'm not 100% sure. I'd prefer to not use anything from matrix multiplication, if that's possible.
[tex]x'^\mu=\Lambda^\mu_\nu x^\nu[/tex]
Would I multiply on the left by:
[tex](\Lambda^{-1})^\nu_\mu[/tex]?
It seems to make sense, but I'm not 100% sure. I'd prefer to not use anything from matrix multiplication, if that's possible.