Let $A \in \mathbb{R}^{n \times n}$, and let $|\cdot|$ denote the Euclidean norm on $\mathbb{R}^n$. For the linear autonomous system
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\begin{align*}
\frac{dx}{dt}=Ax,
\end{align*}
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the equilibrium $0 \in \mathbb{R}^n$ is Lyapunov stable if and only if there exists a constant $M>0$ such that, for every $x \in \mathbb{R}^n$ and every $t \ge 0$,