Let T be a normal operator on a finite-dimensional complex inner product space V. Use
Chapter 6, Problem 7(choose chapter or problem)
Let T be a normal operator on a finite-dimensional complex inner product space V. Use the spectral decomposition AiTi + A2T2 + h XkTk of T to prove the following results. (a) If g is a polynomial, then (b) (c) (d) (e) (f) SCO = >(Ai)T< z=i If T" = To for some n, then T = ToLet U be a linear operator on V. Then U commutes with T if and only if U commutes with each Tj. There exists a normal operator U on V such that U2 = T. T is invertible if and only if Aj ^ 0 for 1 < i < k. T is a projection if and only if every eigenvalue of T is 1 or 0.
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