1
vote
1answer
93 views

R-linear functionals on manifolds

Surely the following is well known: Let $X$ be a (differentiable) manifold, $R$ the ring of continuous/smooth real functions on $X$, $V$ the $R$-module of all continuous/smooth vector fields on ...
1
vote
0answers
15 views

Calculus of final point of a rect/line

I'm creating a little game and i'm trying to calculate the final point to draw the bullet movement. I getting troubles trying to calculate the final point of the line having the bullet vector [-1,0 ...
2
votes
1answer
46 views

On the structure of a vector bundle

Let $P \rightarrow X$ be a principal $G$-bundle, $\rho: G\rightarrow GL(V)$ and $\sigma: G\rightarrow GL(W)$ be two finite dimensional linear representations of $G$. Let $E=P\times_\rho V$ and ...
33
votes
2answers
910 views

Geometric intuition for the tensor product of vector spaces

First of all, I am very comfortable with the tensor product of vector spaces. I am also very familiar with the well-known generalizations, in particular the theory of monoidal categories. I have ...
3
votes
1answer
176 views

Whitney sum of vector bundles

I would like to know how to establish that $ \bigwedge^k ( E \oplus F ) = \bigoplus_{p+q=k} \bigwedge^p E \otimes \bigwedge^q F $ such that $ E $ and $ F $ are two vector bundles. Thanks a lot.
1
vote
1answer
81 views

Vector space structure on $(-1,1) \subset \mathbb{R}$ (or: möbius strip as vector bundle)

I'm first putting the question into it's context, so probably you can see if i'm asking the wrong question to get what i want. The Task is to show that the Möbius (Moebius) strip is a Vector bundle ...
3
votes
0answers
103 views

Which (endo)functors of the category of finite-dimensional real vector spaces induce continuous maps between Hom-sets?

Let $\operatorname{Vect-fin}$ be a category of finite-dimensional vector spaces over $\mathbb{R}$. In this category Hom-sets $\operatorname{Hom}(V,W)$ are themselves finite-dimensional vector spaces ...
0
votes
1answer
75 views

Equation system form to vector form

How can I convert the equation system form of the line to its corresponding vector form? I currently have: $x + y - z = 8$ $2x + 2y + z = 15$ I need the line description in a form of $(a_1, b_1, ...
5
votes
1answer
200 views

Pasting Together Fibers of a Vector Bundle

Everyone: Please forgive that I do not yet know LaTex, bro, and my English ( I am from UCV in Venezuela). I think I understand concept of bundles almost well, and that, once a vector bundle with a ...