Is this an isomorphism between vector spaces

[ak123456]

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 ??

 

[Dick]

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.