- #1
Carl140
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Homework Statement
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??