- #1

- 29

- 0

## Homework Statement

Let U be a vector subspace of C

^{2n}such that

sum(x

_{i}*y

_{i}) = 0 for 1 <= i <= 2n for any x, y ∈ U. Show that dim U <= n. Give an example of such a subspace U with dim U = n

**2. The attempt at a solution**

I tried just writing out the summation and was thinking along the lines of linear independence but I don't think that applies here (maybe it does, I'm not sure). Could I think of a linear map contained in U that maps two vectors x and y to be the sum = 0? I think I'm confusing myself here.