  Let G denote a closed, connected, self adjoint, noncompact subgroup of
GL(n,R), and let d_{R} denote the canonical right invariant Riemannian metric
on G. For v in R^{n} let G_{v} = {g in G : g(v) = v}. We obtain algebraically
defined upper and lower bounds for the asymptotic growth rate of g --> log
|g(v)| / d_{R}(g,G_{v}), and these bounds are sharp if G_{v} is compact. If the
lower bound is positive, then the orbit G(v) is closed in R^{n}. The results
apply to representations of noncompact semisimple Lie groups G on finite
dimensional real vector spaces.
