Let f:V × V → F be a bilinear form on a vector space V, where F is the field of scalars. 3 conditions must be fulfilled:
If F=Q (as the set of rational numbers) then if f fulfills 1. and 2. then it must fulfill 3.
I was wondering how to prove that?
Another question is to find an example of a function/map that is not a bilinear form (and precise on which field it is) because it fulfills 1. and 2. but not 3.
Thanks a lot for any help or suggestions!