(adsbygoogle = window.adsbygoogle || []).push({}); 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??

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# Homework Help: Infinite dimensional counterexample

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