In mathematics and computer programming, index notation is used to specify the elements of an array of numbers. The formalism of how indices are used varies according to the subject. In particular, there are different methods for referring to the elements of a list, a vector, or a matrix, depending on whether one is writing a formal mathematical paper for publication, or when one is writing a computer program.
I've already posted a couple of index notation questions on here and I've gotten very helpful responses. So I thought I'd try my lucky again, though I'm a little more stumped on this question than I was on the others...
Let \vec{x} be the position vector and \vec{r} the radial unit vector. In...
How do I make sense of the index notation expression
r_j r_i p_j
?
What I really *want* it to be is
\vec{r} (\vec{r} \cdot \vec{p})
And it turns into this, as long as I can commute the r_i[/tex] and r_j...right?
(By the way, here \vec{r} is just the position vector and...
I'm trying to simplify the expression
(\hat{r} \times \vec{\nabla}) \times \hat{r},
where \hat{r} is the radial unit vector, using index notation. I think I'm right to write this as:
((\hat{r} \times \vec{\nabla}) \times \hat{r})_i =...
Homework Statement
hey just wondering if anyone could show the the working for the index notation in the attachment it would be greatfully appreciated. thanks. the answer is there I am just looking for the working.
Homework Equations
The Attempt at a Solution
I'm differentiating with respect to Grassman variables, and I'm getting something very inconsistent:
Suppose \xi and \chi are two-component, left-handed, grassman-valued spinors. Now, I take derivatives with of the product, \xi^a \chi_a, respect to \xi two different ways, and denote their...
Homework Statement
Prove vector identity \nabla x\nabla\phi = 0 using index notation.
Homework Equations
\nabla x A = Ejrt\partialrAt
The Attempt at a Solution
I'm treating this as \nablax A, where A = del \Phi = Etpq\partialp\Phiq
putting A back in the equation:
=...
How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.
Hi, does anyone know a link showing how to calculate curl with a Levi-Civita tensor. I can't figure it out but I am sure if I could see an actual example would be able to work out what is going on.
Thanks.
Homework Statement
Find the dual vector of the following tensor:
6 3 1
4 0 5
1 3 2
Homework Equations
dj= EijkTik
Where Eijk = 1 if ijk=123, 231, 312
Eijk = 0 if i=j i=k or j=k
Eijk = -1 if ijk = 132, 213, 321
The Attempt at a Solution
Ok...
This is a brief tutorial to cover the basics of index notation which are useful when handling complicated expressions involving cross and dot products.
I will skip over a lot of technicalities (such as covariant and contravariant vectors) and focus on 3 dimensions - but all of what I say here...
A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you...
I am playing around with learning index notation for tensors, and I came across the following where C is a 0th order tensor:
E_{ijk} \partial_j \partial_k C = 0
I believe this equates to \nabla \times \nabla C. I don't understand why this comes out to 0. Any ideas?
Also, I am trying...
I've been stuck with this problem since a while.. thought I'd ask here;
\nabla \times \dfrac{\vec{A} \times \vec{r}}{2}
solving normally isn't any problem, but I have to do it with index notation, where A is an arbitrary vector field and r is the position vector)
This is how far I can...
hello, i just started learning index notation in my engineering class, and I am having some trouble. one of the problems on my homework was:
putting this in index notation:
\vec{f}=g \frac{m_1m_2}{\vec{r}^2} \ \frac{\vec{r}}{\sqrt{\vec{r}^2}}
and then another problem that reads...