My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 15th, 2018, 05:51 AM   #1
Newbie
 
Joined: Aug 2017
From: Zimbabwe

Posts: 8
Thanks: 0

Question on vector spaces

Could we have two vector spaces, each with its own set of basis vectors, but these basis vectors are related according to the following way? A particular set of vectors in the first vector space may exist "all over the place", but when you represent the same information in the second vector space, the discrete vectors in the first space can still be made out in the second space, but line up end to end to form one composite vector in it.

Last edited by skipjack; March 15th, 2018 at 10:03 AM.
moyo is offline  
 
March 15th, 2018, 05:52 AM   #2
Newbie
 
Joined: Aug 2017
From: Zimbabwe

Posts: 8
Thanks: 0

I was thinking the first set of basis vectors have to be factors of the second.
moyo is offline  
March 24th, 2018, 04:00 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

You seem to have only a vague idea of what a "vector space" is. The only operations in a vector space are vector addition and scalar multiplication. You cannot talk about "factors" of vectors nor does it make sense to talk about vectors "end to end"..
Country Boy is offline  
May 17th, 2018, 09:23 AM   #4
Newbie
 
Joined: Aug 2017
From: Zimbabwe

Posts: 8
Thanks: 0

Quote:
Originally Posted by Country Boy View Post
You seem to have only a vague idea of what a "vector space" is. The only operations in a vector space are vector addition and scalar multiplication. You cannot talk about "factors" of vectors nor does it make sense to talk about vectors "end to end"..

I went back and tried to study a bit more ...but with youtube videos, so forgive me if I am still naive...

I have a few questions that I would appreciate answers for

If I have a vector space of the following form. There is a multidimensional space that these vectors live on, and a particular matrix formed from some vectors has a determinant of zero.

Now are we able to apply curvature to the vector space in order to increase the value of the determinant for zero to something positive? And how would we do this?

Last edited by skipjack; June 18th, 2018 at 09:40 PM.
moyo is offline  
June 18th, 2018, 12:25 PM   #5
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

"Curvature" is not defined for general vector spaces. The determinant formed by taking n vectors in $\displaystyle R^n$ is zero if and only if the vectors are linearly dependent. There is no way to make that determinant non-zero.

Last edited by skipjack; June 18th, 2018 at 09:41 PM.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
question, spaces, vector



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
vector spaces bonildo Linear Algebra 3 September 22nd, 2015 08:14 AM
Vector spaces bamby Linear Algebra 5 January 30th, 2014 02:39 PM
vector spaces, hard question tnewbury12 Linear Algebra 1 February 18th, 2012 03:36 AM
A Question in Normed Vector Spaces Hooman Real Analysis 15 September 1st, 2011 05:01 PM
vector spaces al1850 Linear Algebra 1 March 20th, 2008 10:50 AM





Copyright © 2018 My Math Forum. All rights reserved.