grandes-ecoles 2023 Q22

grandes-ecoles · France · mines-ponts-maths1__psi Matrices Diagonalizability and Similarity
Let $A \in S _ { n } ^ { + + } ( \mathbf { R } )$ and $M \in S _ { n } ( \mathbf { R } )$. Show that $A ^ { - 1 } M$ is similar to a real symmetric matrix.
Hint: You may use question 3.
Let $A \in S _ { n } ^ { + + } ( \mathbf { R } )$ and $M \in S _ { n } ( \mathbf { R } )$. Show that $A ^ { - 1 } M$ is similar to a real symmetric matrix.

Hint: You may use question 3.