grandes-ecoles 2017 QIII.A.4

grandes-ecoles · France · centrale-maths1__mp Invariant lines and eigenvalues and vectors Eigenvalue constraints from matrix properties
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.