- #1
MimuiSnoopy
- 2
- 0
Homework Statement
Let V be a n-dimensional vector space.
Let B: V* x V -> F (field) be the bilinear map defined by B(alpha,v) = alpha(v). Show that B in nondegenerate in the second variable. (4 marks)
Homework Equations
I know that B is non-degenerate in the second variable if; B(alpha,v)=0 for every alpha a member of V* which implies that v=0.
The Attempt at a Solution
My attempt was writing out the definition I know (applying it to the variables given). I do not know how to show that it is true for the bilinear map given.
The other thing I know, but not sure if it helps or not, is that if B is symmetric/skew then we can define the radical so that B is non-degenerate on each variable iff radB={0}. But I'm not sure if I need this or not.
----
I am currently working through some of the past papers I did for my second year units at university, trying to understand the things I couldn't do at the time ready for my third year units. However obviously the university hasn't supplied us with answers yet so I cannot check what I am doing is correct or not. Thank you for your help!
----