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  3. let v be a finite dimensional inner product space and...

Question: let v be a finite dimensional inner product space and...

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Let V be a finite dimensional inner product space and W ⊂ V a subspace. For every v ∈ V there is a unique decomposition v = w + w ′ with w ∈ W and w ′ ∈ W⊥. Define a map T : V → V by Tv = w − w ′ . Prove that T is a unitary and self-adjoint operator.

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