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
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
you have $\displaystyle \phi : \mathbb{R}^n \rightarrow \mathbb{R}_+^{n}$ by $\displaystyle \phi(a_1,...,a_n)=(e^{a_1},...,e^{a_n})$?
This is bijective because $\displaystyle \phi ^{-1} ((a_1, ..., a_n))= (ln(a_1),..., ln(a_n))$
I think you can check it is a morphism.