grandes-ecoles 2020 Q5

grandes-ecoles · France · centrale-maths1__pc Matrices Diagonalizability and Similarity

In the case $n=1$: Let $M$ be a matrix of size $2 \times 2$ that is symmetric and symplectic. Show that $M$ is diagonalizable and that its eigenvalues are inverses of each other. Show that there exists a matrix $P$ that is both orthogonal and symplectic such that $P^{-1} M P$ is diagonal.

In the case $n=1$: Let $M$ be a matrix of size $2 \times 2$ that is symmetric and symplectic. Show that $M$ is diagonalizable and that its eigenvalues are inverses of each other. Show that there exists a matrix $P$ that is both orthogonal and symplectic such that $P^{-1} M P$ is diagonal.

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