grandes-ecoles 2014 Q11

grandes-ecoles · France · x-ens-maths1__mp Not Maths

We assume $\mathbb{K} = \mathbb{R}$. We denote by $O ( n )$ the usual orthogonal group of $\mathbb { R } ^ { n }$ (which identifies with $O _ { n , 0 }$). We denote by $K _ { r , s } : = O _ { r , s } \cap O ( n )$.
Prove that $K _ { r , s }$ is compact and in bijection with $O ( r ) \times O ( s )$.

We assume $\mathbb{K} = \mathbb{R}$. We denote by $O ( n )$ the usual orthogonal group of $\mathbb { R } ^ { n }$ (which identifies with $O _ { n , 0 }$). We denote by $K _ { r , s } : = O _ { r , s } \cap O ( n )$.

Prove that $K _ { r , s }$ is compact and in bijection with $O ( r ) \times O ( s )$.

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