1. The problem statement, all variables and given/known data Let V be a finite dimensional vector space and let W be a subspace of V. 1. Then V is the direct sum of W and W' where W' denotes the orthogonal complement of W. 2. Also, (W')' = W, i.e the orthogonal complement of the orthgonal complement of W is again W. My question is, what happens if we drop the condition that V is finite dimensional, would the results would be still valid? what happens with condition 1 and 2??