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In this note we consider the global convergence properties of thedifferential 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 thepresented results are not new, but scattered throughout literature. Themotivation of this note is to summarize and extend the convergence resultsknown from literature. Rather than giving an exhaustive list of references, theresults are presented in a self-contained fashion.

On the differential equation $\dot{\Theta}=(\Theta^{T}-\Theta)\Theta$ with $\Theta\in{SO(n)}$