Q05. (3+3=6 marks) Let P E Mnxn (R) and let U E Maxn (C). Prove or disprove: (a) If B = {v1, ..., Un} and
Q05. (3+3=6 marks) Let P E Mnxn (R) and let U E Maxn (C). Prove or disprove: (a) If B = {v1, ..., Un} and C = {Pul, ..., Pun} are both orthogonal bases of R", then P is an orthogonal matrix. (b) If B = {v1, . .., Un} and C = {Uv1, . .., Uun} are both orthonormal bases of Cn, then U is a unitary matrix
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