Tagged Questions

4
votes
2answers
70 views

Why distinguish between row and column vectors?

Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a ...
-1
votes
1answer
101 views

Vector Addition — Direction

Say we have three forces $F_1, F_2, F_3$, such that $$ F_1 + F_2 - F_3 = 0\hspace 10mm (1) $$ And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
0
votes
2answers
61 views

Meaning of juxtaposition of vectors

I came across some notation that I can't quite understand: $$ \hat{r}\hat{r} - \textbf{1}_3$$ where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the ...
5
votes
4answers
268 views

Are covariant vectors representable as row vectors and contravariant as column vectors

I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. ...
2
votes
3answers
235 views

How to distinguish 4D and 3D vectors in handwriting?

Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting. In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
2
votes
2answers
59 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
1
vote
2answers
209 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
1
vote
2answers
160 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...