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Suppose that P : V → V is a linear map such that P2 = P....

Suppose that P : V → V is a linear map such that P2 = P. Show that V = range P ⊕ null P.
(Hint: Write v ∈ V as v = P v+(v−P v).) (Remark: P is called a projection or an idempotent.)

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