I am wondering if there is a systematic way to fix the phase of complex eigenvectors. For example [tex]e^{i \theta}(1,\omega,\omega^2)[/tex] where [itex]e^{i \theta}[/itex] is an arbitrary phase and [itex]\omega[/itex] and [itex]\omega^2[/itex] are the cube roots of unity, is an eigenvector of the cyclic matrix [tex]\left(\begin{matrix}0& 1&0\\0&0&1\\1&0&0\end{matrix}\right).[/tex] But I feel that [itex](1,\omega,\omega^2)[/itex] and equivalently [itex](\omega,\omega^2,1)[/itex] and [itex](\omega^2,1,\omega)[/itex] are somehow special because one of the components is real and positive. Is there some special name for such a choice of phase? Any reference will be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# Eigenvectors with at least one positive component

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