grandes-ecoles 2015 Q1

grandes-ecoles · France · x-ens-maths1__mp Matrices Matrix Group and Subgroup Structure

(a) Show that $O _ { n } ( \mathbb { R } )$ is a subgroup of the group $\mathrm { GL } _ { n } ( \mathbb { R } )$ of invertible matrices.
(b) Show that $O _ { n } ( \mathbb { R } )$ is a compact subset of $\mathcal { M } _ { n } ( \mathbb { R } )$.

(a) Show that $O _ { n } ( \mathbb { R } )$ is a subgroup of the group $\mathrm { GL } _ { n } ( \mathbb { R } )$ of invertible matrices.\\
(b) Show that $O _ { n } ( \mathbb { R } )$ is a compact subset of $\mathcal { M } _ { n } ( \mathbb { R } )$.

Paper Questions

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