Question: Let V be a k-dimensional vector space, let W be a subspace of V. Prove that the linear operator proj_W : V->V is one-to-one iff

Let V be a k-dimensional vector space, let W be a subspace of V. Prove that the linear operator proj_W : V->V is one-to-one iff W=V.

(we know: for v V, v W iff proj_W(v) = v)

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