- #1
Damidami
- 94
- 0
Hi,
I'm trying to understand the natural transformation from V to V**, and the book has the theory but I think I'm needing an example.
Lets say V=R^2 a vector space over K=R.
B={(1,1),(1,-1)} a basis of V
B={x/2 + y/2, x/2 - y/2} a basis of V*
v = (3,2) a vector of V
I want to get a vector of V** (a funtional of V*), it is supposed to be
Lf_v = f(v)
with f in V*
But who is f? a generic funtional? let's say
f=ax+by
then
f(v) = 3a + 2b ?
then Lv = 3a + 2b?
And I can't also see how to construct a basis for V**
Please, any help will be appreciated. Thanks!
I'm trying to understand the natural transformation from V to V**, and the book has the theory but I think I'm needing an example.
Lets say V=R^2 a vector space over K=R.
B={(1,1),(1,-1)} a basis of V
B={x/2 + y/2, x/2 - y/2} a basis of V*
v = (3,2) a vector of V
I want to get a vector of V** (a funtional of V*), it is supposed to be
Lf_v = f(v)
with f in V*
But who is f? a generic funtional? let's say
f=ax+by
then
f(v) = 3a + 2b ?
then Lv = 3a + 2b?
And I can't also see how to construct a basis for V**
Please, any help will be appreciated. Thanks!