• Support PF! Buy your school textbooks, materials and every day products Here!

Is this an isomorphism between vector spaces

  • Thread starter ak123456
  • Start date
  • #1
50
0

Homework Statement


a belongs to R
show that the map
L: R^n------R^n>0
(R^n>0 denote the n-fold cartesian product of R>0 with itself)
(a1)
(....) ----------
(an)

(e^a1)
(.....)
(e^an)
is a isomorphism between the vector space R^n and the vector space R^n>0

Homework Equations





The Attempt at a Solution


no idea about this question
any clue ?
can i say because of bijective
a1=e^a1 .......an=e^an ??
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618


I don't get the question. Yes, it is a bijection. But I wouldn't think of (R>0)^n as a vector space in the usual sense. If there's a bijection between two sets you can always say one is the same as the other just by identifying operations in one with operations in the other. But I doubt that's what the question is.
 

Related Threads for: Is this an isomorphism between vector spaces

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
7
Views
2K
Replies
12
Views
2K
  • Last Post
Replies
1
Views
837
  • Last Post
Replies
8
Views
4K
Replies
4
Views
3K
Replies
0
Views
1K
Top