- Summary
- need help for basic calculus

Hi there,

I'm just starting Zee's Einstein Gravity in a Nutshell, and I'm stuck on a seemingly very easy assumption that I can't figure out. On the Tensor Field section (p.53) he develops for vectors x' and x, and tensor R (with all indices being upper indices) : x'=Rx => x=RT x' (because R-1=RT in that case, that's ok) => ∂xk/∂x'h = (RT)kh = Rhk

On page 45 in the Index&Notations section he develops, for vectors u=Mv (M matrix) : ui=Mij vj => dui = Rij dvj (R rotation matrix) => dx'i = Rij dxj

So should not it be ∂xk/∂x'h = Rkh ???

Thanks for enlighting me

I'm just starting Zee's Einstein Gravity in a Nutshell, and I'm stuck on a seemingly very easy assumption that I can't figure out. On the Tensor Field section (p.53) he develops for vectors x' and x, and tensor R (with all indices being upper indices) : x'=Rx => x=RT x' (because R-1=RT in that case, that's ok) => ∂xk/∂x'h = (RT)kh = Rhk

On page 45 in the Index&Notations section he develops, for vectors u=Mv (M matrix) : ui=Mij vj => dui = Rij dvj (R rotation matrix) => dx'i = Rij dxj

So should not it be ∂xk/∂x'h = Rkh ???

Thanks for enlighting me