= Vi O Let T be the linear operator on V that satisfies T(U(v;)) (1 ≤ i ≤ k) and T(w;) = 0 (1 ≤ i ≤ j). Then T is well defined, and T = U*. Hint: Show that (U(x), y) = (x, T(y)) for all x, y € 3. There are four cases. OU* is a partial isometry.

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