[math] \newcommand{\mathds}{\mathbb}[/math]

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Comment on the spectral radius theorem, stating that for a normal operator, [math]TT^*=T^*T[/math], the spectral radius is equal to the norm,

[[math]] \rho(T)=||T|| [[/math]]

with examples and counterexamples, and simpler proofs of well, in various particular cases of interest, such as the finite dimensional one.