grandes-ecoles 2015 Q10b

grandes-ecoles · France · x-ens-maths__pc Matrices Matrix Decomposition and Factorization

In this part, we study the case $n = 2$. For two real numbers $u$ and $v$ such that $u \geqslant v$, we denote: $$S(u, v) = \left\{M \in \mathcal{S}_{2}(\mathbb{R}) \mid s^{\downarrow}(M) = (u, v)\right\}.$$ We fix $b_{1} \geqslant b_{2}$.
Determine a continuous function defined on $[-\pi, \pi]$ whose image equals $S\left(b_{1}, b_{2}\right)$.

In this part, we study the case $n = 2$. For two real numbers $u$ and $v$ such that $u \geqslant v$, we denote:
$$S(u, v) = \left\{M \in \mathcal{S}_{2}(\mathbb{R}) \mid s^{\downarrow}(M) = (u, v)\right\}.$$
We fix $b_{1} \geqslant b_{2}$.

Determine a continuous function defined on $[-\pi, \pi]$ whose image equals $S\left(b_{1}, b_{2}\right)$.

Paper Questions

Q1a Q1b Q1c Q1d Q2a Q2b Q2c Q3a Q3b Q3c Q4a Q4b Q4c Q4d Q5a Q5b Q6a Q6b Q6c Q7a Q7b Q8a Q8b Q8c Q8d Q8e Q9 Q10a Q10b Q10c