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({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Eigenvectors with at least one positive component

**Physics Forums | Science Articles, Homework Help, Discussion**