grandes-ecoles 2014 QII.A.3

grandes-ecoles · France · centrale-maths2__psi Hyperbolic functions
Deduce the equality: $$O ^ { + } ( 1,1 ) = \left\{ \left( \begin{array} { c c } \operatorname { ch } \gamma & \operatorname { sh } \gamma \\ \operatorname { sh } \gamma & \operatorname { ch } \gamma \end{array} \right) , \gamma \in \mathbb { R } \right\} \cup \left\{ \left( \begin{array} { c c } - \operatorname { ch } \gamma & \operatorname { sh } \gamma \\ \operatorname { sh } \gamma & - \operatorname { ch } \gamma \end{array} \right) , \gamma \in \mathbb { R } \right\}$$
Deduce the equality:
$$O ^ { + } ( 1,1 ) = \left\{ \left( \begin{array} { c c } \operatorname { ch } \gamma & \operatorname { sh } \gamma \\ \operatorname { sh } \gamma & \operatorname { ch } \gamma \end{array} \right) , \gamma \in \mathbb { R } \right\} \cup \left\{ \left( \begin{array} { c c } - \operatorname { ch } \gamma & \operatorname { sh } \gamma \\ \operatorname { sh } \gamma & - \operatorname { ch } \gamma \end{array} \right) , \gamma \in \mathbb { R } \right\}$$