Linear Algebra Done Right · Problem 7F.20

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms-normal

Problem

Suppose T∈L(V)T \in \mathcal{L}(V) is normal. Prove that ∥Tk∥=∥T∥k\|T^k\| = \|T\|^k for every positive integer kk.

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