grandes-ecoles 2020 Q31

grandes-ecoles · France · centrale-maths1__pc Matrices Eigenvalue and Characteristic Polynomial Analysis

Let $M \in \mathcal{A}_{2n}(\mathbb{R}) \cap \mathrm{Sp}_{2n}(\mathbb{R})$. Show that all eigenvalues of $M^{2}$ are strictly negative.

Let $M \in \mathcal{A}_{2n}(\mathbb{R}) \cap \mathrm{Sp}_{2n}(\mathbb{R})$. Show that all eigenvalues of $M^{2}$ are strictly negative.