Consider a linear first order differential equation: $$y'=\alpha\bigg(1-\frac{y}{K}\bigg)y$$ where $y, K, \alpha \in \mathbb{R}$. We know the solution for $y'=0$ is at $y=0$ and $y=K$.
Through phase-line plot technique, we know the $y=K$ is asymptotically stable and $y=0$ is unstable. https://en.wikipedia.org/wiki/Phase_line_(mathematics)
Suppose now we consider the above in the matrix case:
$$\dot{R} = AR$$ where $A,R\in \mathbb{R}^{n\times n}$, then how to decide the equilibrium point is stable or not?