A matrix $A$ of $\mathcal{M}_{n}(\mathbb{R})$ is said to be positively stable if all its complex eigenvalues have strictly positive real part. Give an example of a positively stable matrix $A$ such that $A_{s}$ is not positive definite.
A matrix $A$ of $\mathcal{M}_{n}(\mathbb{R})$ is said to be positively stable if all its complex eigenvalues have strictly positive real part.
Give an example of a positively stable matrix $A$ such that $A_{s}$ is not positive definite.