  We introduce a definition of a "localization width" whose logarithm is given
by the entropy of the distribution of particle component amplitudes in the
Lyapunov vector. Different types of localization widths are observed, for
example, a minimum localization width where the components of only two
particles are dominant. We can distinguish a delocalization associated with a
random distribution of particle contributions, a delocalization associated with
a uniform distribution and a delocalization associated with a wave-like
structure in the Lyapunov vector. Using the localization width we show that in
quasi-one-dimensional systems of many hard disks there are two kinds of
dependence of the localization width on the Lyapunov exponent index for the
larger exponents: one is exponential, and the other is linear. Differences, due
to these kinds of localizations also appear in the shapes of the localized
peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the
spatial and momentum parts of the Lyapunov vectors. We show that the Krylov
relation for the largest Lyapunov exponent $\lambda\sim-\rho\ln\rho$ as a
function of the density $\rho$ is satisfied (apart from a factor) in the same
density region as the linear dependence of the localization widths is observed.
It is also shown that there are asymmetries in the spatial and momentum parts
of the Lyapunov vectors, as well as in their $x$ and $y$-components.
