  In this note, we connect two different topics from linear algebra and
numerical analysis: hypocoercivity of semi-dissipative matrices and strong
stability for explicit Runge--Kutta schemes. Linear autonomous ODE systems with
a non-coercive matrix are called hypocoercive if they still exhibit uniform
exponential decay towards the steady state. Strong stability is a property of
time-integration schemes for ODEs that preserve the temporal monotonicity of
the discrete solutions. It is proved that explicit Runge--Kutta schemes are
strongly stable with respect to semi-dissipative, asymptotically stable
matrices if the hypocoercivity index is sufficiently small compared to the
order of the scheme. Otherwise, the Runge--Kutta schemes are in general not
strongly stable. As a corollary, explicit Runge--Kutta schemes of order $p\in
4\N$ with $s=p$ stages turn out to be \emph{not} strongly stable. This result
was proved in \cite{AAJ23}, filling a gap left open in \cite{SunShu19}. Here,
we present an alternative, direct proof.
