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Let T : V → V be a linear operator satisfying T2 = T. Define U1...

Let T : V → V be a linear operator satisfying T2 = T. Define U1 = {v ∈ V : T(v) = v} and U2 = {v ∈ V : T(v) = 0}. Prove that V = U1 ⊕ U2.

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