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## Homework Statement

Let ##S## be a subspace of an inner product space ##V##. Prove that ##V=S\oplus S^{\bot}##.

## Homework Equations

The circled plus is meant to indicate the orthogonal sum of two sets.

From an earlier exercise, I've shown that ##S^{\bot}## is a subspace of ##V##, and that ##S\cap T = \{ 0\}## (where ##S\bot T##). Don't know if they'll be helpful to this proof, but I'll leave these results up if they will be.

## The Attempt at a Solution

I don't know where to begin. I've resorted to looking online for established proofs, but even those don't make sense to me. Could someone help me along with this proof? Thanks.