- #1
Noobnoob
- 8
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- TL;DR 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