# Tagged Questions

Use this tag for questions about specific tensors (curvature tensor, stress tensor), or questions regarding tensor computations as they appear in multivariable calculus and differential/Riemannian geometry (specifically, when it is amenable to be treated as objects with multiple indices that ...

13 views

### Infinitesimal Strain Tensor in a Cubic Crystal

I'm currently working through Vectors and Tensor in Engineering and Physics, and there's a problem regarding the strain tensor that I'm having a bit of trouble with. Given a cubic crystal with zero ...
26 views

### Series Relation

$\{A_n\}$ is a sequence of 4th order tensors. $lim_{n\rightarrow\infty}A_n = O_4$, where $O_4$ is the null 4th order tensor. The series $\sum_{n=1}^{\infty}A_n$ converge to a known tensor $B$. I ...
25 views

30 views

### Understanding metric tensor notation

I am trying to understand if there is a conventional way to read super- and subscript notation of metric tensors. Is there a canonical way of doing this? For instance, what is the difference between ...
58 views

41 views

### How to handle the tensor $T^i_{ljk}$, given that $T^i_{jkl}=3T^i_{ljk}$?

$T^i_{~~jkl}$ is a tensor such that $T^i_{~~jkl}=3T^i_{~~ljk}$ is some coordinate system. Prove that $T^i_{~~jkl}=3T^i_{~~ljk}$ in all coordinate systems. The given answer says: \begin{align} \bar T^...
19 views

### Contracting a symmetric tensor product with a covector

What I actually want to ask is about a problem of specific form, which I could not put in the title as I'm not certain on any short name for such problems. For given a rank-2 tensor $K^{\mu\nu}$ and ...
26 views

### Translation by tensors

According to this question, quaternions would not be the right choice to handle both rotation and translation. In the case of tensors, one might assert that the rotation would be possible by tensors, ...
38 views

### Given the parallel and perpendicular component of a vector in terms of another vector, how do you determine the tensor that connects both?

Sorry for the awkwardly phrased title, I wasn't sure how to properly word it. I want to do the following: I have a vector $\vec J$ and a vector $\vec E$ with the following relation (with the ...
54 views

### How can we visualize a tensor?

I would greatly appreciate it if someone could explain to me how to visualize a tensor in the analogous way that we visualize a vector. Thanks!
41 views

### How do I get from the universal product of the tensor product to other definitions.

I was wondering how you can "derive" the common (or "classical") definition of the tensor product before the universal property was established (I think there is no need to repeat it here), i.e. a ...
54 views

### Solve for third rank linear tensor equation $C_{[ij]k}U^jU^k=A_i$

Is there a way to solve a general tensor equation of the form, written in an arbitrary frame $$C_{[ij]k}U^jU^k=A_i,$$ for a tensor field $C$ of type $(0,3)$ (the square ...
53 views

13 views

### benefit of trifocal geometry vs bifocal geometry?

I am at the moment trying to understand what kind of benefit I would have by using three cameras for stereo vision rather than two cameras? I mean, i would only have more constraints related to the ...
25 views

### Transformation of fourth rank tensor and its matrix form

I would like to calculate transformation of fourth rank tensor, $$C_{ijkl}=\Sigma_{m=1}^{3}\Sigma_{n=1}^{3}\Sigma_{p=1}^{3}\Sigma_{q=1}^{3}a_{im}a_{jn}a_{kp}a_{lq}C_{mnpq}$$ where $a_{xy}$ is ...
38 views

### How do I compute the gradient of a tensor?

From this paper, we have three matrices $U\in \mathbb{R}^{n\times d_U}$, $M\in \mathbb{R}^{m\times d_m}$, $C\in \mathbb{R}^{c\times d_C}$ and a tensor $S\in \mathbb{R}^{d_U \times d_M \times d_C}$, ...