grandes-ecoles 2020 Q23

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

Let $M \in \mathcal{S}_{2n}(\mathbb{R}) \cap \mathrm{Sp}_{2n}(\mathbb{R})$. What about $E_{-1}$? (i.e., does $E_{-1}$ have even dimension and does there exist an orthonormal basis of $E_{-1}$ of the form $(X_{1}, \ldots, X_{p}, J_{n} X_{1}, \ldots, J_{n} X_{p})$?)

Let $M \in \mathcal{S}_{2n}(\mathbb{R}) \cap \mathrm{Sp}_{2n}(\mathbb{R})$. What about $E_{-1}$? (i.e., does $E_{-1}$ have even dimension and does there exist an orthonormal basis of $E_{-1}$ of the form $(X_{1}, \ldots, X_{p}, J_{n} X_{1}, \ldots, J_{n} X_{p})$?)

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