= Unitary transitions of the tautological line over the projective line
{title2=$g_{01}(\zeta)=|\zeta|/\zeta$}
For $\zeta=z_2/z_1$ and $\eta=1/\zeta$, the tautological frames $(1,\zeta)$ and $(\eta,1)$ differ by $1/\zeta$. Normalize their ambient <Hermitian form> norms; the resulting frames differ by the displayed phase. The unit circle total space is $S^3\subset\mathbb C^2$ and its projection to the <complex projective line> is the <Hopf fibration>. The transition of the dual line is the reciprocal phase.
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