Homomorphism from Hom(W, F) to Hom(V, F)

1,357
0
The problem statement, all variables and given/known data
Let T be a homomorphism from V into W. Using T, define a homomorphism T* of Hom(W, F) into Hom(V, F).


Note on notation
Hom(V, F) is just the dual space of V. Similarly for Hom(W, F).


The attempt at a solution
This is a problem from Hernstein's "Topics in Algebra". It is given before the sections covering linear independence, bases and dual spaces, which I find odd. I don't have much to work with here. The only T* I can define at this point is the one sending everything in Hom(W, F) to the 0 functional in Hom(V, F). Any tips?
 

Dick

Science Advisor
Homework Helper
26,249
611
Pick a w in Hom(W,F). So w:W->F. You want T*(w) to map V->F. There's a natural way to use T:V->W to do that.
 
1,357
0
OOhhh....I see it know. Thanks a bunch.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top