Register to reply 
Strange vector spaces 
Share this thread: 
#1
Feb2013, 12:42 AM

P: 332

What are some of the strangest vector spaces you know? I don't know many, but I like defining V over R as 1 tuples. Defining vector addition as field multiplication and scalar multiplication as field exponentiation. That one's always cool. Have any cool vector spaces? Maybe ones not over R but over maybe more exotic fields?



#2
Feb2013, 01:04 AM

C. Spirit
Sci Advisor
Thanks
P: 5,427

R over Q is infinite dimensional. That's kinda cool I guess :p.



#3
Feb2013, 01:11 AM

P: 332




#4
Feb2013, 03:52 AM

Sci Advisor
HW Helper
P: 4,300

Strange vector spaces
I also liked it when I realised that some sets functions are a vector space and you can basically think of them as ntuples (for [itex]n = 2^{\aleph_0}[/itex]). Was the first time I saw that vector spaces don't need to consist of actual points in [itex]\mathbb{R}^k[/itex].



#5
Feb2013, 07:03 PM

Sci Advisor
HW Helper
PF Gold
P: 3,171

In general, I thought it was really cool when starting to learn about field extensions, the epiphany that we can view the larger field as a vector space over the smaller one, and now we can bring in all the machinery of linear algebra to develop the theory. That was a great "ah HA!!" moment. 


Register to reply 
Related Discussions  
Linear spaces vs. vector spaces  Linear & Abstract Algebra  19  
Vector Spaces: Verify whether a set is a vector space  Calculus & Beyond Homework  1  
Position vector and tangent vector in Riemannian spaces  Differential Geometry  13  
Vector spaces: column spaces  Calculus & Beyond Homework  1  
Vector Spaces / Sub Spaces  Linear & Abstract Algebra  4 