Tagged Questions

0
votes
0answers
37 views

Einstein notation non-repeating indices

I forget the rule for Einstein notation. If I have something like the gradient: $$\vec\nabla f = \frac{\partial f}{\partial x_i} = \langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial ...
2
votes
2answers
41 views

Tensor notation and rules

I have a few questions about tensors: I appreciate that $g^{\alpha\beta}=g^{\beta\alpha}$ but when contracting say $T^{\sigma}_{\mbox{ }\;\mu\nu\rho}$ to $T_{\;\;\mu\nu}$, first of all can it be ...
2
votes
1answer
123 views

Understanding tensor divergence notation in an integral

Given a smooth tensor valued function $\sigma:R^2\rightarrow R^{2\times2}$, I'm trying to show that $\int_\Omega \nabla\cdot\sigma=\int_{\partial\Omega}\sigma n$, where $\Omega$ is a connected ...
1
vote
0answers
68 views

Confusion with vectors and notation

Could someone please explain to me why $$\nabla (\dot{r}\cdot A)$$ take the following form in index notation? $$\left({\partial A_i\over \partial r^k}-{\partial A_k\over \partial ...
1
vote
1answer
128 views

Index notation clarification

Previously, I have seen matrix notation of the form $T_{ij}$ and all the indices have been in the form of subscripts, such that $T_{ij}x_j$ implies contraction over $j$. However, recently I saw ...
1
vote
1answer
144 views

What's are these index objects called? And $\mathrm{\LaTeX}$ \sum question

I want to refer to $$A_iB_jC_k$$ using $$\psi(ijk) = A_iB_jC_k$$ So that I can write out quite overwhelming-looking sums of ABC terms as sums of terms that look like 123, 231, 113, etc. If I am not ...
3
votes
0answers
132 views

Better Tensor Notation

I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of ...
1
vote
1answer
196 views

Index/Einstein notation to derive Gibbs/Tensor relations

In a few continuum classes I have seen indicial notation used to derive relations in Gibbs notation. However, Gibbs notation is valid for all coordinates while indicial notation is valid only for ...
5
votes
2answers
201 views

Index notation for tensors: is the spacing important?

While reading physics textbooks I always come across notation like: $$J_{\alpha}^{\quad\beta},\ \Gamma_{\alpha \beta}^{\quad \gamma}, K^\alpha_{\quad \beta}.$$ Notice the spacing in indices. I can't ...
2
votes
2answers
200 views

Tensors of order 3

I'm wondering what a tensor of order 3 looks like, and what it's purposes are. I've seen them written down before, but they look like matrices; I'm probably not understanding the concept well. How is ...
1
vote
1answer
356 views

Einstein notation - difference between vectors and scalars

From Wikipedia: First, we can use Einstein notation in linear algebra to distinguish easily between vectors and covectors: upper indices are used to label components (coordinates) of ...