grandes-ecoles 2010 QIIE2

grandes-ecoles · France · centrale-maths2__pc Matrices Diagonalizability and Similarity

We assume in this question that $\mathbb { K }$ is equal to $\mathbb { R }$.
Show that two non-zero matrices of $\mathcal { M } _ { 0 } ( 2 , \mathbb { R } )$ are similar in $\mathcal { M } ( 2 , \mathbb { R } )$ if and only if they have the same characteristic polynomial.

We assume in this question that $\mathbb { K }$ is equal to $\mathbb { R }$.

Show that two non-zero matrices of $\mathcal { M } _ { 0 } ( 2 , \mathbb { R } )$ are similar in $\mathcal { M } ( 2 , \mathbb { R } )$ if and only if they have the same characteristic polynomial.

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