  The $\eta$ transition form factor is analysed for the first time in both
space- and time-like regions at low and intermediate energies in a
model-independent approach through the use of rational approximants. The
$\eta\rightarrow e^+e^-\gamma$ experimental data provided by the A2
Collaboration in the very low energy region of the dilelectron invariant mass
distribution allows for the extraction of the most precise up-to-date slope and
curvature parameters of the form factors as well as their values at zero and
infinity. The impact of these new results on the mixing parameters of the
$\eta$-$\eta^\prime$ system, together with the role played by renormalisation
dependent effects, and on the determination of the $VP\gamma$ couplings from
$V\to P\gamma$ and $P\to V\gamma$ radiative decays are also discussed.
