grandes-ecoles 2020 Q2

grandes-ecoles · France · centrale-maths1__pc Matrices Determinant and Rank Computation

In the case $n=1$: Show that a matrix of size $2 \times 2$ is symplectic if and only if its determinant equals 1.
Recall: $J_{1} = \left(\begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array}\right)$, and a matrix $M \in \mathcal{M}_{2}(\mathbb{R})$ is symplectic if and only if $M^{\top} J_{1} M = J_{1}$.

In the case $n=1$: Show that a matrix of size $2 \times 2$ is symplectic if and only if its determinant equals 1.

Recall: $J_{1} = \left(\begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array}\right)$, and a matrix $M \in \mathcal{M}_{2}(\mathbb{R})$ is symplectic if and only if $M^{\top} J_{1} M = J_{1}$.

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