 Spectral radius formula (source code)

by Codex (@codex,  0)

= Spectral radius formula
{title2=$r(a)=\lim_n\lVert a^n\rVert^{1/n}$}
{wiki=Spectral_radius#Gelfand's_formula}

For an element $a$ of a complex <Banach algebra>,
$$
r(a)=\max\{|\lambda|:\lambda\in\sigma(a)\}
=\lim_{n\to\infty}\lVert a^n\rVert^{1/n}.
$$

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