Tensors Definition and 376 Threads

U[/Color]s[/Color]i[/Color]n[/Color]g[/Color] [/Color] T[/Color]e[/Color]n[/Color]o[/Color]r[/Color]s[/Color] i[/Color]n[/Color] t[/Color]h[/Color]i[/Color]s[/Color] F[/Color]o[/Color]r[/Color]u[/Color]m[/Color] W[/Color]h[/Color]a[/Color]t[/Color]...

Is there any relationship between tensors, as they're used in diff geo and the notion of tensor product as used in module theory? I seem to recall that tensor products were "invented" because, given a field k and U, V two vector spaces over k such that dim U=n, dim V=m, we wanted to construct a...

I wonder if anyone might have some suggestions for a good self-study book on tensors. I'm just starting in on Jackson and have only seen tensors briefly in my previous undergrad classes. Any suggestions?

Why do we say that the position 4-vector, x^{\mu}, is naturally contravariant and that the del operator, \partial_{\mu}, is naturally covariant? The only thing I could come up with is that the contravariant del components \partial^{\mu} = (-c^{-1}\partial_t,\nabla) have a negative sign in...

What a tensor is .? I have found a text in my book that says that the electric and magnetic constants are tensors.. Do u have something in mind? Thx a lot

Hello everyone, this seems like a great forum here with a lot of knowlegable people and I was hoping someone could help me out with this question. I'm an engineering student and I've recently decided to switch into physics. Now I'm trying to catch up on the math I'm going to need, so I'm...

Greetings Gurus, I'm sure this has been asked before, so feel free to redirect me. What is the connection between tensors in physics and tensoring in algebra? That is, could anyone sketch the path between them? Thanks, Kevin

Can anyone recommend good introductory texts for self-study? I want to teach myself about tensors and about topology. FYI, I have a B.S. in Physics and am a Fellow of the Casualty Actuarial Society. I don't remember my vector calculus and am in the process of relearning - I'm using the book...

q1 What is rank of a tensor? q2 I don't know why after contraction operation (or trace of tensor) the rank of a tensor will be reduced by 2? q3 I can't imagiant how the fourth rank tensor, e^iklm looks like? q4 What does an anti-symmetric tensor e^iklm means? Is it a 4 by 4 martix or a...

could someone please explain the difference or non-difference of matrices and tensors? i come across the two plenty in various fields of physics and am curious. i have a feeling this question has been asked and answered before, but i could not find a previous thread, so pointing me to another...

I'm having trouble with this question. It's from Rindler's Introduction to Special Relativity which I'm going through myself. I'm just starting to learn about tensors. <<<<i) A vector A^i has components \dot{x}, \dot{y} in rectangular Cartesian coordinates; what are its components in polar...

show that B_{ij} can be written as the sum of a symmetric tensor B^S_{ij} and an antisymmetric tensor B^A_{ij} i don't know how to do this one. for a symmetric tensor we have B^S_{ij} = B^S_{ji} and for an antisymmetric tensor we have B^A_{ij} = -B^A_{ji} the only thing my book...

inertia tensors (moment of inertia) for a game Hello, physics gurus! I'm trying to write a little 2D game that uses physics for more dynamism. Part of this game involves shapes bouncing around and reacting to forces, each other, etc. Each shape that can interact is a set of one or more...

I have some simple questions on how to write matrices as tensors. 1. \left(\begin{array}{cc}a_1\\a_2\end{array}\right)+ \left(\begin{array}{cc}b_1\\b_2\end{array}\right)= \left(\begin{array}{cc}c_1\\c_2\end{array}\right) is this equivalent to A^j + B^j = C^j with j = 1,2...

I'm on the verge of ripping my hair out :mad: I understand the basics of tensors but I just can't get my head around the need have having contra and covariant vectors.. what is the point??! A vector is a vector right? why have a sub and superscripts why can't they just stick to one or the...

Hi all, I have 2 tensors of rank 2. I want to write their product in a way else than a matrix. Or let's say, for example: how can I write the electic field in a form of matrix (tensor)? Thanks

I've already handed in my (I can only assume) incorrect solution, but I just felt like posting, though I'm not sure if anyone will be able to help. I have a rank-2 covariant tensor, T sub i,j. This can be written in the form of t sub i,j + alpha*metric tensor*T super k, sub k (I hope my...

Tensors & Differential Geometry -- What are lie groups? I've heard a lot about "lie groups" on this section of the forum, and was wondering what they are and if someone could explain it in simple terms. Thank you.

whats a good intro book to tensors and manifolds?

I'm reading in on the subject of General Relativity and came across a few things I don't understand. First of all I'm not sure where the following rule comes from, and maybe someone can explain or derive it for me: \eta^{\mu \beta} h_{\nu \sigma,\beta} = h_{\nu \sigma}^{,\mu} And I also...

Hi all. This is my first post. w00t! I'm just starting my sophmore year at university an I am trying to get ahead in physics, however I have hit a roadblock on tensors. I read all your posts in the 'what is a tensor' threads and I have a little better idea of what a tensor is, but I am...

I once read that tensors may be considered a special class of a more general class of entities called 'holors.' It was just a parenthetical comment; no further information was supplied. Can anybody fill me in on this topic? In what sense is holor a generalization of tensor? What branches of...

What began as a highly motivated inquiry into understanding Special Relativity has come to a grinding halt on Tensors. I hadn't heard the term before yesterday; now I've spiraled so far away from the topic of SR that I'm wholly determined to learn Tensors FIRST because I believe they're very...

Event Vector: [ sec, m, m, m ] or [sec, light-sec, ..] 00th component of metric tensor : m^2/sec^2. iith components of metric tensor : 1. 0ith or i0th components of metric tensor: m/sec. 4-velocity: [ 1, m/sec, .. ] 4-momentum; [kg, kg*m/sec, .. ] 4-Force : [ kg/sec, kg*m/sec^2...

Let \mathbf{S} = \mbox{$\frac {1}{2}$}(\sigma_1 + \sigma_2) be the total spin of a system of two spin-(1/2) particles. a) Show that \mathbf{P} \equiv (\mathbf{S} \cdot \mathbf{r})^2 / {r^2} is a projection operator b) Show that tensor operator S_1_2 = 2(3P - \mathbf{S}^2) satisfies S_1_2...

In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions: Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold? How is this group defined in matrix algebra? Is it a subgroup of GL(4). How do...