Can the Angle Between Two 7-Dimensional Vectors Be Calculated?

  • Thread starter Thread starter robertjford80
  • Start date Start date
  • Tags Tags
    Angles
robertjford80
Messages
388
Reaction score
0
Apparently you can calculate the angle between two vectors even when they occupy say 7 dimensions. I have trouble believing that. To me if a vector occupies 7 dimensions than it is incommensurable with another vector occupying 7 dimensions.
 
Physics news on Phys.org
Two non-collinear vectors span a 2-dimensional plane, no matter how many dimensions they are embedded in. The angle between the vectors is measured in that plane.
 
robertjford80 said:
Apparently you can calculate the angle between two vectors even when they occupy say 7 dimensions. I have trouble believing that. To me if a vector occupies 7 dimensions than it is incommensurable with another vector occupying 7 dimensions.
First, I don't understand what you mean by a vector "occupying" 7 dimensions. A vector is, pretty much by definition, a one dimensional object, no matter what the dimension of the underlying space. Perhaps that is your misunderstanding. You may be think of the vector as "taking up" the entire space. That is not true in 7 dimensions any more than it is true in 3 dimensions. You are talking about vector s in 7 dimensions, not "occupying" 7 dimensions.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I What are the significant angles between intersecting planes in 4D space?
Replies
26
Views
3K
B Parametric Representation of Lines
Replies
13
Views
3K
I Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
Replies
5
Views
3K
I Angle between two vectors with many dimensions
Replies
12
Views
4K
I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional
Replies
40
Views
2K
A Performing MLEM with Response Matrix for 4pi Imager and 1x3 Vector Input
Replies
1
Views
2K
I Non orthogonal basis and the lines of its coordinate grid
Replies
9
Views
3K
B Question about orthogonal vectors and the cosine
Replies
5
Views
2K
I Terminologies used to describe tensor product of vector spaces
Replies
7
Views
3K
I Standard basis and other bases...
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top