grandes-ecoles 2015 Q2

grandes-ecoles · France · x-ens-maths1__mp Invariant lines and eigenvalues and vectors Diagonalizability determination or proof

Let $M$ and $N$ be in $S _ { n } ( \mathbb { R } )$. Show that there exists $U \in O _ { n } ( \mathbb { R } )$ such that $N = U M U ^ { - 1 }$, if and only if $\chi _ { M } = \chi _ { N }$.

Let $M$ and $N$ be in $S _ { n } ( \mathbb { R } )$. Show that there exists $U \in O _ { n } ( \mathbb { R } )$ such that $N = U M U ^ { - 1 }$, if and only if $\chi _ { M } = \chi _ { N }$.

Paper Questions

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