  Let $G$ be a Lie group $G$ with representation $\rho$ on a real simple
$G$-module $\mathbb{V}$. We will call the orbits of the induced action of
$\rho$ on the projectivization $P\mathbb{V}$ the projective orbits, and
projective orbits of lowest possible dimension will be called minimal. We show
that when $G$ is semi-simple and non-compact, there exists a compact subgroup
$K\subset G$ such that the minimal orbits of $G$ are in bijection with the
minimal $K$-orbits on a $K$-invariant proper subspace $\mathbb{W}\subset
\mathbb{V}$. In the case that $G$ is split-real, $K$ is the trivial subgroup
and there is a unique closed projective orbit, which is moreover of minimal
dimension.
