2
votes
2answers
72 views

Square vs non-square tensors?

In mathematics, tensors are objects that operates on vector space. In physics or engineering, tensors usually operates on one vector space and its dual space: $V^{*} \times V^{*} \times V^{*} \times ...
2
votes
1answer
89 views

Putting Maxwell's Equations in Tensor Form. (Carroll Chapter 1 Question 11)

Simply put, if you look at https://en.wikipedia.org/wiki/Electromagnetic_tensor#Significance it says you can go from the traditional four "vector calculus" maxwell equations to two tensor Maxwell ...
1
vote
1answer
43 views

Non-square tensors?

I learnt tensor algebra for physics and I never saw a non-square (or non-cubic...) tensor. But, from a mathematical point of view, do non-square tensors exist? And if so, are they used in some area in ...
0
votes
2answers
104 views

Tensor Projection

I'm currently reading "Vector and Tensor Analysis with Applications" by A.I. Borisenko and I.E. Tarapov, and I'm having trouble following a particular mathematical step in where the author projects ...
3
votes
1answer
69 views

Non commutative tensor products / simple example?

In O'Neil's "Semi-Riemannian Geometry" it is stated that if $A$ is a $(r,0)$-tensor field and $B$ is $(0,s)$-tensor field then it is ""from the definition'' that $A \otimes B = B \otimes A$. I still ...
1
vote
1answer
86 views

Maxwells Equations in a curvilinear coordinate system

I was wondering if anyone would be able to explain to me how the author goes from equation 3 to equations 4(a,b,c) in this paper. I am confused how to treat the contravariant metric tensor in these ...
2
votes
1answer
139 views

Tensors in math and physics

I know how tensor product f two modules is defined in communtative algebra. But there is also a concept of tensors used in physics. Are these two concepts related? If yes, can someone explain me ...
4
votes
1answer
339 views

Torque calculation, to achieve clean spin+tumble

Here's a pencil-like robotic spaceship carrying an experiment, it is a solid mass 100m long, 100 inches thick and weighs 1000kg. We're in deep solar space 100au above the sun. Assume we can apply ...
0
votes
0answers
84 views

Is there a rigorous exposition of 'tensor methods' for finding lie group representations?

I've seen tensor methods in physics for finding lie group representations, as in Wu-Ki Tungs Group Theory in Physics, which uses tensors physics style, ie with indices; and Cvitonovics Birdtracks, ...
6
votes
2answers
321 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 ...