Talk:General Relativity/Rigorous Definition of Tensors

This page seems to switch the conventions for indices; previous pages say that upper indices represent contravariant vectors and that lower indices represent vectors. Is there any reason for the apparent inconsistency here? Luolimao (discuss • contribs) 14:13, 18 May 2013 (UTC)

Lost
$$\mathbf{T} \left( \mathbf{\sigma}, \mathbf{u} \right) = T^\mu_{\ \nu} \mathbf{e}_\mu \otimes \mathbf{d}x^\nu \left( \sigma_\alpha \mathbf{d}x^\alpha, u^\beta \mathbf{e}_\beta \right) = T^\mu_{\ \nu} \mathbf{e}_\mu \left( \sigma_\alpha \mathbf{d}x^\alpha \right) \mathbf{d}x^\nu \left( u^\beta \mathbf{e}_\beta \right) = T^\mu_{\ \nu} \sigma_\alpha u^\beta \delta^\alpha_\mu \delta^\nu_\beta = T^\mu_{\ \nu} \sigma_\mu u^\nu $$


 * 1) Where did $$\mathbf{\sigma} = \sigma_\alpha \mathbf{d}x^\alpha$$  come from?
 * 2) What does $$\mathbf{d}x$$ mean?  Differential operator? What is the x?

Sorry lost.

Thepigdog (discuss • contribs) 08:25, 3 June 2014 (UTC)