  We investigate possible systematic errors in the recent measurement of the
matter power spectrum from the Lyman-alpha forest by Croft et al. (2001). We
find that for a large set of prior cosmological models the Croft et al. result
holds quite well, with systematic errors being comparable to random ones, when
a dependence of the recovered matter power spectrum on the cosmological
parameters at z~3 is taken into account. We find that peculiar velocities cause
the flux power spectrum to be smoothed over about 100-300 km/s, dependng on
scale. Consequently, the recovered matter power spectrum is a smoothed version
of the underlying true power spectrum. Uncertainties in the recovered power
spectrum are thus correlated over about 100-300 km/s. As a side effect, we find
that residual fluctuations in the ionizing background, while having almost no
effect on the recovered matter power spectrum, significantly bias estimates of
the baryon density from the Lyman-alpha forest data. We therefore conclude that
the Croft et al. result provides a powerful new constraint on cosmological
parameters and models of structure formation.
