  We discuss the determination of the linear power spectrum of dark matter
fluctuations from measurements of the transmitted flux Ly-alpha Forest power
spectrum. We show that at most scales probed by current measurements, the flux
power spectrum is significantly affected by non-linear corrections to the
linear dark matter power spectrum due to gravitational clustering. Inferring
the linear dark matter power spectrum shape is therefore difficult due to
non-linear corrections driving the non-linear power spectrum to a k^{-1.4}
shape nearly independent of initial conditions. We argue that some methods used
in previous estimates underestimate the uncertainties in the shape of the
linear dark matter power spectrum.
