  In this note we consider the global convergence properties of the
differential equation $\dot{\Theta}=(\Theta^{T}-\Theta)\Theta$ with
$\Theta\in{SO(n)}$, which is a gradient flow of the function
$f:SO(n)\rightarrow\mathbb{R},\Theta\mapsto{2n-2\tr{\Theta}}$. Many of the
presented results are not new, but scattered throughout literature. The
motivation of this note is to summarize and extend the convergence results
known from literature. Rather than giving an exhaustive list of references, the
results are presented in a self-contained fashion.
