132. (Roman, 10.8) Let V be a finite-dimensional inner product space and let T L(V) be...

 

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132. (Roman, 10.8) Let V be a finite-dimensional inner product space and let T L(V) be a normal operator. (a) Prove that if T is idempotent, then T is also self-adjoint. (b) Prove that if T is nilpotent (T = 0 for some n > 1) then T = 0. (c) Prove that if T2 = 73, then T is idempotent. 132. (Roman, 10.8) Let V be a finite-dimensional inner product space and let T L(V) be a normal operator. (a) Prove that if T is idempotent, then T is also self-adjoint. (b) Prove that if T is nilpotent (T = 0 for some n > 1) then T = 0. (c) Prove that if T2 = 73, then T is idempotent.