  We carry out extensive computer simulations to study the Lyapunov instability
of a two-dimensional hard disk system in a rectangular box with periodic
boundary conditions. The system is large enough to allow the formation of
Lyapunov modes parallel to the x axis of the box. The Oseledec splitting into
covariant subspaces of the tangent space is considered by computing the full
set of covariant perturbation vectors co-moving with the flow in tangent-space.
These vectors are shown to be transversal, but generally not orthogonal to each
other. Only the angle between covariant vectors associated with immediate
adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the
probability of this angle to vanish approaches zero. The stable and unstable
manifolds are transverse to each other and the system is hyperbolic.
