Let U be a unitary matrix. Prove that (a) U is normal. (b) _Ux_ = _x_ for all x Cn. (c)

Chapter 6, Problem 15

(choose chapter or problem)

Let U be a unitary matrix. Prove that (a) U is normal. (b) _Ux_ = _x_ for all x Cn. (c) if is an eigenvalue of U, then || = 1. 1

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